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Today, we're going
to take it quite easy.

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I also have to take it
a little easy

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because my voice may be petering
out, if I'm not careful.

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We're going to apply today
what we have learned,

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so there is nothing new
but its applications.

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And that's important-- things
that... you can let it sink in.

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We have here a trajectory

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of a golf ball
or a tennis ball in 26.100.

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We shoot it up
at an angle alpha.

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The horizontal component
in the x direction

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is v zero cosine alpha

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and the vertical component
is v zero sine alpha.

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It reaches
the highest point at P

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and it returns to the ground
at point S.

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This is
the increasing y direction

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and this is
the increasing x direction.

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We're going to use,
very heavily,

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the equations that you see here
that are so familiar with us.

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These are the one-dimensional
equations in x direction

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where there is no acceleration

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and the one-dimensional
equations in the y direction

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where there is acceleration.

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In order to use these equations

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we need all these constants--

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x zero, v zero x and v zero y.

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We have seen those last time.

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I choose for x zero...
I choose zero arbitrarily.

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Also for y zero.

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The velocity in the x direction
will never change.

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This v zero x will always remain
v zero cosine alpha.

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The velocity in the y direction,
however, in the beginning

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at t equals zero
is v zero sine alpha.

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And that one will change,
because there is here this t

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and that's why the velocity
is going to change.

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This t will do it.

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And the acceleration
in the y direction--

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since this is
increasing value of y--

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is going to be negative 9.8.

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Since I call always 9.8 plus...

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since I always call g
"plus 9.8," this is minus g.

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I now want to ask first

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the question that you may
never have seen answered:

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what is the shape of this?

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Well, we can go to
equation number three there

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and we can write down
this equation number three:

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That y, as a function of time,
equals v zero yt

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so it is v zero sine alpha
times t

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minus one-half gt squared.

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That's the equation in y.

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I go to equation number one

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and I write down x--
at any moment in time--

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equals v zero z times t

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so that is
v zero cosine alpha times t.

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Now I eliminate t,

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and the best way to do that
is to do it here--

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to write for t, x divided
by v zero cosine alpha.

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Now I can drop
all subindexes t

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because we're now going
to see x versus y.

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We're going to eliminate t.

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So this time here, I'm going to
substitute in here and in there

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and so I'm going
to get y equals...

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There's a v zero here

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and there's a v zero there
that cancels.

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There's a sine alpha here
and a cosine alpha there

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that makes it a tangent
of alpha.

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And then I have here the x

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and I get minus one-half g
times this squared--

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x squared divided by v zero
cosine alpha squared.

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And now look very carefully.

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Y is a constant times x

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minus another constant
times x squared.

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That is a parabola.

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It's a second-order equation
in x, and is a parabola

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and a parabola has this shape.

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So you so see now,
by eliminating the time

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that we have here a parabola.

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Now I want to massage
this quite a bit further today.

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I would like to know

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at what time the object here

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comes to a halt
to its highest point.

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It comes to a halt
in the y direction.

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It comes to a highest point

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and I want to know
how high that is.

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Well, the best way to do
is to go to equation four

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and you say, to equation four,

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"When are you zero?"

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Because that is the moment

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that the velocity

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in the y direction becomes zero.

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It must be
at its highest point, then.

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So in order to find, for us,

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the position
of the highest point P

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we first ask ourselves

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the question
from equation number four:

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when is the velocity
in the y direction zero?

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And that then becomes
v zero y

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which is v zero sine alpha
minus gt

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and out pops that t at point P

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is going to be v zero sine alpha
divided by g.

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That's the time that it takes

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for the object
to reach the highest point.

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Where is it, then?

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What is the highest point
above the ground?

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Well, now we have to go
to equation number three

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and you have to substitute
this time in there

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so that highest point h,

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which is y at the time t of P
equals v zero yt--

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that is v zero
times the sine of alpha.

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But you have to multiply
it by this time

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and so I get
another v zero sine alpha

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and I get a g here
minus gt mi...

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oh, no, no, this equa...
minus half dt squared

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minus one-half g
times this one squared

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which is v zero
sine alpha squared,

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divided by g...
divided by g squared

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because there is a g here,
you see?

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So you square the whole thing
if it's t squared.

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You lose one g

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and you will find, then,
that the highest point--

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let's write it down here so that
we don't block that blackboard--

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the highest point in the sky

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equals v zero sine alpha squared
divided by 2g.

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That is the highest point.

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Let's give that some color

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because we may want
to keep that.

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Is it reasonable that the point,
the highest point in the sky

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gets higher when v zero
is higher?

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Of course.

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If I shoot it up
at a higher speed

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of course it will get higher.

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So that's completely intuitive
that v zero is upstairs.

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If I increase the angle
from a small angle

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to larger and larger and larger

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is it reasonable
that it will get higher?

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Of course.

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You all feel in your stomach

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that the highest possible value
you can get

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is when you make alpha
90 degrees for a given velocity.

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That's the highest it will go
in the sky.

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So clearly, this is
also very pleasing.

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If you did the experiment
on the moon

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with the same initial speed,
it will go much higher

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so you are also happy to see
that this g here is downstairs.

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So that makes sense.

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At what time will the object
be at point S?

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Now, there are two ways
that you can do that.

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You either go to this equation,
number three

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and you ask equation number
three, "When are you zero?"

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It will give you two answers.

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It will say, "I am zero here
at this time"

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and "I am zero at that time."

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And those are the two times
that you want

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and this is the one you pick.

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That's perfectly fine.

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I think there's a faster way to
do it, and that's the following.

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This is a parabola,

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so it's completely symmetric
about the vertical, about P.

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So to climb up from O to P must
take the same amount of time

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as to go down from P to S

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and so I claim
that the time to reach point S

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must be twice the time
to reach point P

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and therefore it's going to be

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two v zero sine alpha
divided by g.

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But now we want to look again

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whether the v zeros and the sine
alphas have the right place.

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Indeed, if I increase the speed,

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I would expect it to take longer
before it reaches S.

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If I give it a larger speed,
it will come out farther

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and obviously,
the time will take longer.

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If I do it at a higher angle,
it will also take longer

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and if I do it on the moon,
it will also take longer.

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So this makes sense--

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these equations are pleasing
in terms of the rate

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that v zero and sine alpha
appear in the equations.

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But now comes
an important point

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which I am going to use
throughout this lecture.

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I want to know what OS is.

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The distance OS... I shoot it up
and it hits the floor again

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What is that distance
that it travels?

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Well, for that,
I need equation number one.

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It is v zero x times the time

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and v zero x
is v zero cosine alpha.

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We got v zero cosine alpha
times the time to hit it--

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that is two v zero sine alpha.

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So I get a two here, I get a
sine alpha, and I get a g here

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and I have another v zero there,
and so the answer is

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a v zero squared times
the sine of the double angle--

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remember, two cosine
alpha sine alpha

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is the sine of two alpha--
divided by g.

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And this is OS, and I'm going
to need this a lot.

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This reminds me
not to remove it.

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Now, I sort of wonder,
and you should too

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why is it that the highest point
in the sky has a v zero squared

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and why is
the farthest point also...

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why does it also have
a v zero squared?

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There must be a way
that you can reason that.

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Why is it not just v zero?

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Why is it v zero squared?

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Well, I'll let you argue
about the highest points,

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and I'll give you a good reason
for the distance, OS.

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Don't look at the equations.

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You simply...

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Think for a change.

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Don't look at the equations.

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I double the speed.

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If I double the speed,
then it's quite reasonable

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that the time that it takes

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for the object to reach
the ground will double,

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but while the time
that it flies has doubled

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the horizontal velocity
has also doubled.

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And so the distance that it will
travel in horizontal direction

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is four times that-- twice
because the time has doubled

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and another factor of two

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because the horizontal component
has also doubled.

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So that's why you see
v zero squared there--

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completely pleasing.

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This tells you immediately
that the...

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if you want to throw a ball
as far as possible--
 

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people who play baseball
know that--

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you should do it at 45 degrees.

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Because if you throw it
at 45 degrees

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then this angle, 90 degrees,
and that is one.

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Of course, in reality,

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the baseball player
knows better.

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They give effect to the ball,
they deal with air drag

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they spin the ball, and then
these equations are not valid.

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This is only in case we deal
with... with vacuum.

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00:13:46 --> 00:13:52

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I now would like to test

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some of the results
that we have here...

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we have worked out here.

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I am going to shoot a pellet...
a metal ball.

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I'm going to shoot it
at various angles:

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30 degrees, 60 degrees,
45 degrees

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and I'm going to make
a prediction

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if I shoot it up from there,
where it will hit the table.

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A measurement is meaningless

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without knowing
the uncertainties.

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So that's the first thing
we have to deal with.

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The first thing I want to know

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is what is the velocity
of this bullet

245
00:14:32 --> 00:14:38
when it comes out of the spring

246
00:14:34 --> 00:14:40
and does it vary if I do it
three, five, six times in a row?

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00:14:38 --> 00:14:44
It's not a $20,000 spring gun,
so it is likely to vary.

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And the way I am going to do
that is as follows.

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00:14:48 --> 00:14:54

250
00:14:50 --> 00:14:56
If I shoot an object
vertically up--

251
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that is, the maximum value
that it can go--

252
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and with an alpha
equals 90 degrees

253
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then the sine of alpha is one

254
00:15:04 --> 00:15:10
and the height is v zero squared
divided by two g.

255
00:15:09 --> 00:15:15

256
00:15:11 --> 00:15:17
In other words,
if I measure the height

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if I shoot it up vertically

258
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and you can measure
that for me--

259
00:15:19 --> 00:15:25
you will see how I am asking
you to do that--

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then we can calculate
v zero squared.

261
00:15:23 --> 00:15:29
So the first thing I want to do
is to shoot it up vertically

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and how are you going
to help me to calculate...

263
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to tell me how high it is?

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00:15:35 --> 00:15:41
That comes easier
than you think.
 

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The top part...
oh, we'll remove this.

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00:15:44 --> 00:15:50
The top part of this stick
is three meters, the top mark.

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That very top mark
is three meters

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and all I want you to tell me

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00:15:58 --> 00:16:04
whether it is yay much above
or yay much below

270
00:16:01 --> 00:16:07
and then we'll estimate
that yay much

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and then we'll make a guess.

272
00:16:05 --> 00:16:11
And I'll do it twice.

273
00:16:07 --> 00:16:13

274
00:16:08 --> 00:16:14
So if you are ready?

275
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Make sure that you
can distinguish

276
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between above and below--
it makes a big difference, yeah?

277
00:16:15 --> 00:16:21

278
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Okay?

279
00:16:19 --> 00:16:25
Three, two, one, zero.

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00:16:22 --> 00:16:28
(ball whooshes )

281
00:16:23 --> 00:16:29
Okay, was it higher or lower?

282
00:16:25 --> 00:16:31
CLASS:
Higher.

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00:16:26 --> 00:16:32
LEWIN:
How much?

284
00:16:27 --> 00:16:33
This much?

285
00:16:28 --> 00:16:34
Do we agree?

286
00:16:29 --> 00:16:35
Let's say
five centimeters, right?

287
00:16:31 --> 00:16:37
We're going to allow
for an uncertainty.

288
00:16:34 --> 00:16:40
I'll do it again.

289
00:16:36 --> 00:16:42
I want to see
how well it reproduces.

290
00:16:38 --> 00:16:44

291
00:16:39 --> 00:16:45
Three, two, one, zero.

292
00:16:42 --> 00:16:48
(ball whooshes )

293
00:16:44 --> 00:16:50
(students shout out answers )

294
00:16:46 --> 00:16:52
Lower?

295
00:16:47 --> 00:16:53
STUDENT:
Higher.

296
00:16:48 --> 00:16:54
LEWIN:
Higher!

297
00:16:49 --> 00:16:55
So it was 10 centimeters,
five centimeters higher

298
00:16:53 --> 00:16:59
so we'll take seven.
 

299
00:16:56 --> 00:17:02
So we'll make seven

300
00:16:57 --> 00:17:03
and we'll have to allow
for an uncertainty.

301
00:16:59 --> 00:17:05
So h max... is about 3.07.

302
00:17:10 --> 00:17:16
I've done this
this morning 20 times

303
00:17:13 --> 00:17:19
and there were times
that the heights differed

304
00:17:16 --> 00:17:22
by more than 10 centimeters,
sometimes even 15 centimeters.

305
00:17:20 --> 00:17:26
I therefore would feel
most comfortable

306
00:17:25 --> 00:17:31
if you allow me an uncertainty

307
00:17:28 --> 00:17:34
of 15 centimeters
in that height.

308
00:17:32 --> 00:17:38
Remember, once we start shooting
at 30 degrees, there is no way

309
00:17:35 --> 00:17:41
that we can evaluate
the velocity anymore.

310
00:17:37 --> 00:17:43
We have to just take
this value at face value.

311
00:17:40 --> 00:17:46
This is the way we've measured
v zero, and that's it.

312
00:17:46 --> 00:17:52
This is a five percent error,
five percent.

313
00:17:52 --> 00:17:58
So what now is v zero squared?

314
00:17:56 --> 00:18:02
Well, that's easy
to calculate now.

315
00:18:00 --> 00:18:06
V zero squared equals
3.07 times 2 times 9.8...

316
00:18:10 --> 00:18:16
Oh, my calculator was off; 
that's a detail.

317
00:18:16 --> 00:18:22
Um, 3.07 times 2 times 9.8--
that is 60.17.

318
00:18:22 --> 00:18:28
I'd like you to check that.

319
00:18:25 --> 00:18:31
60.17 plus an error
of five percent.

320
00:18:28 --> 00:18:34
That is an error of three

321
00:18:31 --> 00:18:37
so you might as well make
this 60.2.

322
00:18:34 --> 00:18:40
Would you please confirm that,
that I didn't make a mistake?

323
00:18:40 --> 00:18:46
3.07 is h max-- I multiplied
by two, by 9.9, and 60.2

324
00:18:45 --> 00:18:51
There's a five percent error

325
00:18:49 --> 00:18:55
and a five percent error
is indeed three.

326
00:18:53 --> 00:18:59
This is meters squared
per second squared.

327
00:18:57 --> 00:19:03
I don't care what v zero is

328
00:19:00 --> 00:19:06
because if we are going
to measure OS

329
00:19:03 --> 00:19:09
all I need is v zero squared.

330
00:19:05 --> 00:19:11
And if you at home
are going to calculate

331
00:19:07 --> 00:19:13
what the height will be
at the various angles

332
00:19:10 --> 00:19:16
all you need is v zero squared.

333
00:19:12 --> 00:19:18
So I am not even interested
in v zero.

334
00:19:14 --> 00:19:20
I'll just stick
to v zero squared

335
00:19:16 --> 00:19:22
and v zero squared will have
exactly the same uncertainty.

336
00:19:19 --> 00:19:25
It will have an uncertainty
of five percent

337
00:19:22 --> 00:19:28
because it comes immediately
from h.

338
00:19:24 --> 00:19:30
We are not going to change that.

339
00:19:26 --> 00:19:32

340
00:19:28 --> 00:19:34
Okay, so, so much for the
uncertainty in v zero squared.

341
00:19:33 --> 00:19:39
Now I'm going to set
the angle at 45 degrees

342
00:19:36 --> 00:19:42
but how accurately
can I do that?

343
00:19:40 --> 00:19:46
I don't think I can do that
any better than one degree.

344
00:19:45 --> 00:19:51
I'll try to do the best I can.

345
00:19:47 --> 00:19:53
I can't really guarantee you
that I'm accurate to one degree.

346
00:19:51 --> 00:19:57
So now comes the question

347
00:19:54 --> 00:20:00
what happens with
the sine of two alpha

348
00:19:59 --> 00:20:05
because we're going
to measure OS?

349
00:20:03 --> 00:20:09
What happens with
the sine of two alpha?

350
00:20:08 --> 00:20:14
The sine of 90 degrees
is 1.0000.

351
00:20:12 --> 00:20:18
But what would be
the sine of 88 degrees?

352
00:20:15 --> 00:20:21
That is the value
that I cannot exclude

353
00:20:19 --> 00:20:25
if I'm off by one degree.

354
00:20:21 --> 00:20:27
And that value is 0.9994.

355
00:20:25 --> 00:20:31
That is so close to one

356
00:20:30 --> 00:20:36
that it is only off
by 0.6%... 0.06 percent.

357
00:20:37 --> 00:20:43
And that is so low, compared
to five percent, forget it.

358
00:20:43 --> 00:20:49
Forget the error in alpha.

359
00:20:44 --> 00:20:50
We can completely forget it.

360
00:20:46 --> 00:20:52
There's a reason for that.

361
00:20:49 --> 00:20:55
When alpha is 45 degrees,
then 2 alpha is 90 degrees

362
00:20:53 --> 00:20:59
and the sine curve goes
like this at 90 degrees.

363
00:20:58 --> 00:21:04
It's almost flat here.

364
00:20:59 --> 00:21:05
So even if you're off
an angle by a little bit

365
00:21:02 --> 00:21:08
you're still very close to one--
that's the reason.

366
00:21:05 --> 00:21:11
So all we have to worry about

367
00:21:07 --> 00:21:13
is the uncertainty
in v zero squared.

368
00:21:09 --> 00:21:15
And so now comes
my big prediction.

369
00:21:12 --> 00:21:18
I'm going to make
a prediction now:

370
00:21:14 --> 00:21:20
for 45 degrees,
OS equals v zero squared.

371
00:21:28 --> 00:21:34
We have that.

372
00:21:29 --> 00:21:35
That is 60.2.

373
00:21:31 --> 00:21:37
And we have the sine
of two alpha is one

374
00:21:36 --> 00:21:42
and we divide by 9.8.

375
00:21:38 --> 00:21:44
That is 6.14 meters

376
00:21:46 --> 00:21:52
with an uncertainty
of five percent, right?

377
00:21:48 --> 00:21:54
Because that is the uncertainty
in v zero squared

378
00:21:51 --> 00:21:57
and so there is an uncertainty

379
00:21:53 --> 00:21:59
of 30 centimeters,
actually 31 centimeters.

380
00:21:56 --> 00:22:02
This is my prediction
for an angle of 45 degrees.

381
00:22:05 --> 00:22:11
This will only hold
if there is no air drag

382
00:22:09 --> 00:22:15
or if the air drag
is negligible,

383
00:22:12 --> 00:22:18
and of course,
equally important,

384
00:22:16 --> 00:22:22
that that spring gun--
when the ball comes out--

385
00:22:19 --> 00:22:25
that the velocity squared
is indeed within the range

386
00:22:23 --> 00:22:29
that we have assumed

387
00:22:24 --> 00:22:30
and that it doesn't have
bad days and good days.

388
00:22:28 --> 00:22:34
There's no way
I can check that anymore.

389
00:22:32 --> 00:22:38
All right, so we're going
to mark the .614.

390
00:22:36 --> 00:22:42
This is one meter, two meters,
three meters, four meters

391
00:22:42 --> 00:22:48
five meters, six meters, 6.14.

392
00:22:46 --> 00:22:52
One four... 14 centimeters.

393
00:22:49 --> 00:22:55
Boy, God, it's
all the way here.

394
00:22:53 --> 00:22:59
And then I allow for an error
of about 30 centimeters.

395
00:23:00 --> 00:23:06
Did I do that right?

396
00:23:01 --> 00:23:07
That is correct, 45 degrees
with 30 centimeter uncertainty.

397
00:23:06 --> 00:23:12
That is all the way up to here.

398
00:23:10 --> 00:23:16
And then the next one,
roughly 30 centimeters.

399
00:23:16 --> 00:23:22
So that's where, if our
calculations make sense

400
00:23:21 --> 00:23:27
that's where
the ball should hit.

401
00:23:25 --> 00:23:31
Now I would like you
to come here, if you don't mind.

402
00:23:29 --> 00:23:35
Stand here, and the moment
that that ball hits...

403
00:23:33 --> 00:23:39
(whooshes )

404
00:23:34 --> 00:23:40
point your finger at it.

405
00:23:36 --> 00:23:42
Don't do it before I shoot,
but just after I shoot.

406
00:23:39 --> 00:23:45
And then we'll hope
for the best, yeah?

407
00:23:45 --> 00:23:51
Okay.

408
00:23:46 --> 00:23:52
You're not nervous, right?

409
00:23:48 --> 00:23:54
Where... what happened
with that ball that I had?

410
00:23:51 --> 00:23:57
Did I put it in my pocket?

411
00:23:53 --> 00:23:59

412
00:23:56 --> 00:24:02
Oh, it's here.

413
00:23:57 --> 00:24:03
Thank you.

414
00:23:59 --> 00:24:05
So I'm going to set it now, to
the best I can, at 45 degrees.

415
00:24:04 --> 00:24:10

416
00:24:09 --> 00:24:15
And so I can never shoot it any
further, this is the angle...

417
00:24:16 --> 00:24:22
this is
the maximum possible distance.

418
00:24:20 --> 00:24:26
You ready?

419
00:24:23 --> 00:24:29
You are?

420
00:24:25 --> 00:24:31
Don't look at me, look there.

421
00:24:28 --> 00:24:34
It goes fast.

422
00:24:29 --> 00:24:35
Three, two, one, zero.

423
00:24:31 --> 00:24:37
(gun clicks )

424
00:24:32 --> 00:24:38
LEWIN:
Put your finger there!

425
00:24:34 --> 00:24:40
(class laughs )

426
00:24:35 --> 00:24:41
Isn't that fantastic?

427
00:24:38 --> 00:24:44
Isn't that amazing?

428
00:24:40 --> 00:24:46
Do you see now
how important it is

429
00:24:42 --> 00:24:48
that you have uncertainties
in your measurements?

430
00:24:44 --> 00:24:50
In high school, you would have
said it has to hit there.

431
00:24:47 --> 00:24:53
Boom, man, it has an error.

432
00:24:49 --> 00:24:55
(class laughs )

433
00:24:50 --> 00:24:56
And the error has to
be taken into account.

434
00:24:53 --> 00:24:59
Where's my ball, by the way?

435
00:24:55 --> 00:25:01

436
00:24:57 --> 00:25:03
Boy...

437
00:24:59 --> 00:25:05
Oh, I have it, ooh, here.

438
00:25:01 --> 00:25:07

439
00:25:03 --> 00:25:09
(grunts )
 

440
00:25:05 --> 00:25:11
Okay, you can sit down now.

441
00:25:06 --> 00:25:12
You did great.

442
00:25:07 --> 00:25:13
It worked just because
you were there.

443
00:25:09 --> 00:25:15
(class applauds )

444
00:25:15 --> 00:25:21
Now I wonder what happens if
I fire the ball at 30 degrees?

445
00:25:23 --> 00:25:29
If I do it at 30 degrees, then
my v zero squared is the same.

446
00:25:33 --> 00:25:39
I don't have to worry
about that, I hope.

447
00:25:36 --> 00:25:42
However, I cannot be certain
about the angle

448
00:25:39 --> 00:25:45
to better than one degree.

449
00:25:42 --> 00:25:48
So you will say, "Well,
come on now, don't be decadent.

450
00:25:48 --> 00:25:54
"I mean, here we had an error
of only 0.06 percent

451
00:25:51 --> 00:25:57
"because of this one degree...
possible one degree offset.

452
00:25:56 --> 00:26:02
Let's just ignore
this error, too."

453
00:25:58 --> 00:26:04
Ooh... that is risky.

454
00:26:00 --> 00:26:06
That is risky, now
because the sine of 60 degrees--

455
00:26:06 --> 00:26:12
that's what you deal with--

456
00:26:09 --> 00:26:15
the sine of 60 degrees,
I think, is 0.866.

457
00:26:15 --> 00:26:21
That's right.

458
00:26:16 --> 00:26:22

459
00:26:19 --> 00:26:25
But the sine of 58 degrees

460
00:26:22 --> 00:26:28
which is possible
if I'm one degree under

461
00:26:28 --> 00:26:34
~is 0.848, and that is
substantially lower.

462
00:26:35 --> 00:26:41
And therefore I must allow

463
00:26:37 --> 00:26:43
for an uncertainty
in the sine of the angle

464
00:26:41 --> 00:26:47
by roughly, oh, maybe
something like 17 or 18 units--

465
00:26:46 --> 00:26:52
0.0... what is this difference?

466
00:26:50 --> 00:26:56
0.018.

467
00:26:54 --> 00:27:00
If you want to check
what the sine of 62 degrees is

468
00:26:58 --> 00:27:04
you will see that that is about
this much higher than this

469
00:27:03 --> 00:27:09
so we must allow for this error.

470
00:27:05 --> 00:27:11
And that is an error which is
by no means negligible anymore.

471
00:27:14 --> 00:27:20
There's no point here.

472
00:27:16 --> 00:27:22
That is an error which is
18 divided by 866.

473
00:27:19 --> 00:27:25
That is a two percent error.

474
00:27:22 --> 00:27:28
So now we're dealing,
all of a sudden

475
00:27:24 --> 00:27:30
with a two percent error
in the sine of two alpha

476
00:27:28 --> 00:27:34
even though there is only
one degree of uncertainty

477
00:27:32 --> 00:27:38
in the angle.

478
00:27:34 --> 00:27:40
And the reason is
that a sine curve is like so.

479
00:27:37 --> 00:27:43
So a small angle change here
makes no difference

480
00:27:40 --> 00:27:46
but a small angle change here
makes a lot of difference.

481
00:27:43 --> 00:27:49
And that's the reason

482
00:27:45 --> 00:27:51
and you can see that it is
the slope of the sine curve

483
00:27:48 --> 00:27:54
that gives you
a much larger error

484
00:27:51 --> 00:27:57
if you are off
by a teeny-weeny, little bit.

485
00:27:54 --> 00:28:00
So now we are ready
to make a prediction.

486
00:27:57 --> 00:28:03
So here comes the prediction.

487
00:28:00 --> 00:28:06

488
00:28:03 --> 00:28:09
OS now for 30 degrees...

489
00:28:07 --> 00:28:13

490
00:28:11 --> 00:28:17
So I have to go through v zero
squared-- I have that, 60.2

491
00:28:19 --> 00:28:25
and then I have to multiply
by the sine of two alpha

492
00:28:23 --> 00:28:29
that is, the sine of 60...
multiply...

493
00:28:29 --> 00:28:35
and then I think
I have to divide by g.

494
00:28:34 --> 00:28:40
That is right, 9.8,
and I find 5.31, plus or minus.

495
00:28:41 --> 00:28:47
Now, two percent error
in the sine of two alpha

496
00:28:46 --> 00:28:52
five percent error
in v zero squared

497
00:28:49 --> 00:28:55
that gives me-- I can't
help it-- a seven percent error.

498
00:28:54 --> 00:29:00
So I have a seven percent
uncertainty, multiply by .07

499
00:28:59 --> 00:29:05
so I cannot trust this
any better than 37 centimeters.

500
00:29:05 --> 00:29:11
And so now I'm going to put
the markers out

501
00:29:10 --> 00:29:16
at five meters
and 31 centimeters.

502
00:29:12 --> 00:29:18
This is the five-meter mark,
31 centimeters

503
00:29:18 --> 00:29:24
and I allow for 37 centimeters
on either side.

504
00:29:23 --> 00:29:29
It's here... and 37 centimeters
on this side, that is here.

505
00:29:30 --> 00:29:36
I'm going to set the angle
to 30 degrees.

506
00:29:36 --> 00:29:42
Yeah, yeah, come here.

507
00:29:38 --> 00:29:44
We need woman power here.

508
00:29:41 --> 00:29:47
(class laughs )

509
00:29:42 --> 00:29:48
Stay here.

510
00:29:44 --> 00:29:50
Stay out of the fire line,
and when that ball hits

511
00:29:48 --> 00:29:54
you jump on it,
yeah, you jump on it.

512
00:29:51 --> 00:29:57
Okay, everything under control

513
00:29:53 --> 00:29:59
Five... make sure
I marked it right,

514
00:29:56 --> 00:30:02
five meters, three one,
that looks about okay.

515
00:29:59 --> 00:30:05
And now I have to change
the angle to 30 degrees.

516
00:30:04 --> 00:30:10
(grunts )

517
00:30:05 --> 00:30:11

518
00:30:11 --> 00:30:17
Okay, this is as close
as I can do it.

519
00:30:13 --> 00:30:19

520
00:30:16 --> 00:30:22
Okay, you ready?

521
00:30:18 --> 00:30:24
You are?

522
00:30:19 --> 00:30:25
Three, two, one...

523
00:30:23 --> 00:30:29
(ball whooshes )

524
00:30:24 --> 00:30:30
(Lewin shouts )

525
00:30:25 --> 00:30:31
Lewin:
Hit the jackpot!

526
00:30:28 --> 00:30:34
(class cheers and applauds )

527
00:30:32 --> 00:30:38

528
00:30:38 --> 00:30:44
Incredible.

529
00:30:39 --> 00:30:45
What you can argue now,
and successfully--

530
00:30:42 --> 00:30:48
you could say
perhaps you have been

531
00:30:44 --> 00:30:50
a little too conservative on
your errors, and I admit that.

532
00:30:49 --> 00:30:55
But believe me

533
00:30:50 --> 00:30:56
when I did this morning
this five, six times

534
00:30:53 --> 00:30:59
that the error in v zero
was quite substantial.

535
00:30:56 --> 00:31:02
The high differences were
sometimes 15 centimeters

536
00:31:00 --> 00:31:06
and so I had no choice.

537
00:31:02 --> 00:31:08
But it looked like we were
a bit on the conservative side.

538
00:31:05 --> 00:31:11
Suppose, now, I repeated
this experiment at 60 degrees.

539
00:31:10 --> 00:31:16
What will change?

540
00:31:12 --> 00:31:18

541
00:31:17 --> 00:31:23
What will change?

542
00:31:19 --> 00:31:25
Will OS change?

543
00:31:21 --> 00:31:27
No, because the sine
of 120 degrees

544
00:31:24 --> 00:31:30
is the same as the sine
of 60 degrees.

545
00:31:28 --> 00:31:34
You have two alpha here.

546
00:31:30 --> 00:31:36
The sine of 60 is the same
as the sine of 120.

547
00:31:34 --> 00:31:40

548
00:31:36 --> 00:31:42
If you allow for an uncertainty
of one degree on either side
 

549
00:31:40 --> 00:31:46
you will find
exactly these same numbers

550
00:31:42 --> 00:31:48
because of the symmetry
of the sine curve.

551
00:31:45 --> 00:31:51
So again, you are off
by two percent-- no difference.

552
00:31:50 --> 00:31:56
And so this prediction
is unchanged.

553
00:31:52 --> 00:31:58
However, I want
to ask you one question

554
00:31:55 --> 00:32:01
to see whether you are
half-alert or half-asleep.

555
00:31:59 --> 00:32:05

556
00:32:01 --> 00:32:07
At 30 degrees, you saw this.

557
00:32:05 --> 00:32:11
At 60 degrees, giving it
the same initial speed

558
00:32:10 --> 00:32:16
you will see this.

559
00:32:11 --> 00:32:17

560
00:32:14 --> 00:32:20
It will have to hit here

561
00:32:15 --> 00:32:21
within the uncertainty
of our measurements

562
00:32:17 --> 00:32:23
at the same location.

563
00:32:18 --> 00:32:24
It will, of course,
go much higher.

564
00:32:21 --> 00:32:27
You can calculate that because
you will have to use this

565
00:32:25 --> 00:32:31
for the equation for the height

566
00:32:27 --> 00:32:33
and that goes
with the sine of alpha.

567
00:32:30 --> 00:32:36
The sine of alpha for 60 degrees
is way higher than 30 degrees.

568
00:32:35 --> 00:32:41
But now comes a question--

569
00:32:37 --> 00:32:43
will this trajectory
take longer than this one

570
00:32:41 --> 00:32:47
or will they take
the same amount of time?

571
00:32:45 --> 00:32:51
Who is for
the same amount of time?

572
00:32:47 --> 00:32:53

573
00:32:49 --> 00:32:55
Who is for longer?

574
00:32:51 --> 00:32:57
Who is for shorter?
 

575
00:32:53 --> 00:32:59

576
00:32:55 --> 00:33:01
Okay.

577
00:32:56 --> 00:33:02
I am happy
with one set of figures

578
00:32:58 --> 00:33:04
and unhappy
with another set of figures.

579
00:33:03 --> 00:33:09
What is the horizontal velocity

580
00:33:07 --> 00:33:13
of the golf ball
when it takes off?

581
00:33:11 --> 00:33:17
If the velocity is the same
in both cases

582
00:33:14 --> 00:33:20
can't you see that
this horizontal component

583
00:33:18 --> 00:33:24
is way larger
than this horizontal component?

584
00:33:23 --> 00:33:29
And if they travel
the same distance

585
00:33:25 --> 00:33:31
then this tripmust take longer

586
00:33:28 --> 00:33:34
because it's the horizontal
component in the x direction

587
00:33:32 --> 00:33:38
that determines how long it will
take to go from here to there.

588
00:33:38 --> 00:33:44
Suppose I shot it straight up.

589
00:33:41 --> 00:33:47
How long do you think
it will take to hit here?

590
00:33:43 --> 00:33:49

591
00:33:45 --> 00:33:51
It has no horizontal component,
all right?

592
00:33:49 --> 00:33:55
So think about this--
this trajectory will take longer

593
00:33:53 --> 00:33:59
but it ends up
at the same point.

594
00:33:55 --> 00:34:01
All right, number three.

595
00:33:58 --> 00:34:04
Can you come here?

596
00:34:00 --> 00:34:06
So I don't have
to change these markers.

597
00:34:03 --> 00:34:09
They're all perfect

598
00:34:05 --> 00:34:11
provided that nature is
willing to reproduce itself.

599
00:34:10 --> 00:34:16
60 degrees...

600
00:34:11 --> 00:34:17

601
00:34:18 --> 00:34:24
So he'll go way higher,

602
00:34:20 --> 00:34:26
but if all goes well, it should
hit within the same marks.

603
00:34:27 --> 00:34:33
Ready?

604
00:34:29 --> 00:34:35
Three, two, one, zero.

605
00:34:30 --> 00:34:36
(ball whooshes )

606
00:34:32 --> 00:34:38
(ball whacks table )

607
00:34:35 --> 00:34:41
LEWIN:
Here, man.

608
00:34:37 --> 00:34:43
Yeah, here, right?

609
00:34:38 --> 00:34:44
Thank you very much.

610
00:34:39 --> 00:34:45
Wonderful! Look!

611
00:34:41 --> 00:34:47
Maybe my uncertainties
were not so dumb.

612
00:34:43 --> 00:34:49
We were just lucky here
with the jackpot.

613
00:34:46 --> 00:34:52
It's comfortably within
the error, but close to this one

614
00:34:50 --> 00:34:56
so I am quite happy that I took
the uncertainties the way I did.

615
00:34:54 --> 00:35:00
Can we recover the ball?

616
00:34:56 --> 00:35:02
Did someone see it take off?

617
00:34:59 --> 00:35:05
Oh, yeah.

618
00:35:00 --> 00:35:06
All right, now we will enter a
different part of this lecture.

619
00:35:09 --> 00:35:15
which is actually
a very... a very sad part.

620
00:35:15 --> 00:35:21

621
00:35:21 --> 00:35:27
You know that people in Africa
shoot monkeys.

622
00:35:27 --> 00:35:33

623
00:35:32 --> 00:35:38
There is a monkey here
in a tree--

624
00:35:40 --> 00:35:46
very happy.

625
00:35:42 --> 00:35:48
(class laughs )

626
00:35:46 --> 00:35:52
LEWIN:
And here is a hunter...

627
00:35:52 --> 00:35:58
who never took 801

628
00:35:55 --> 00:36:01
and he has a gun,
which is a golf ball gun

629
00:36:02 --> 00:36:08
and he aims that gun
right at the monkey.

630
00:36:09 --> 00:36:15
He shoots it with a certain
velocity, the golf ball.

631
00:36:13 --> 00:36:19
Let this be speed v zero,
so the horizontal component--

632
00:36:20 --> 00:36:26
you're going to see that
again and again--

633
00:36:25 --> 00:36:31
v zero cosine alpha

634
00:36:28 --> 00:36:34
and the vertical component
equals v zero sine alpha.

635
00:36:35 --> 00:36:41
Let this be
my increasing value of y

636
00:36:40 --> 00:36:46
and this be
my increasing value of x.

637
00:36:45 --> 00:36:51

638
00:36:48 --> 00:36:54
This golf ball...
this... this golf gun,

639
00:36:52 --> 00:36:58
is really not first-class,
thank goodness.

640
00:36:57 --> 00:37:03
And so when the hunter shoots
this golf ball, this happens.

641
00:37:03 --> 00:37:09

642
00:37:06 --> 00:37:12
And it ends up here at point p.

643
00:37:11 --> 00:37:17
Lucky monkey, so far.

644
00:37:14 --> 00:37:20
Now, it is very tragic but true

645
00:37:18 --> 00:37:24
that when the monkey sees the
flash of the gun, it lets go.

646
00:37:24 --> 00:37:30
(class laughs )

647
00:37:29 --> 00:37:35
And now comes the question--

648
00:37:31 --> 00:37:37
is the monkey safe or is this
the last day of the monkey?

649
00:37:36 --> 00:37:42
(class laughs )

650
00:37:39 --> 00:37:45

651
00:37:41 --> 00:37:47
I ask the following question.

652
00:37:44 --> 00:37:50
This would be trajectory
with no gravity

653
00:37:49 --> 00:37:55
and this is the trajectory
with gravity.

654
00:37:54 --> 00:38:00
We can both agree on that.

655
00:37:57 --> 00:38:03
At a certain moment, t1,

656
00:37:59 --> 00:38:05
let us assume
that the golf ball

657
00:38:02 --> 00:38:08
would have been here
without gravity.

658
00:38:06 --> 00:38:12
Then I know exactly
where it is with gravity.

659
00:38:11 --> 00:38:17
It must be exactly here

660
00:38:16 --> 00:38:22
because the x position, xt1,
is the same

661
00:38:20 --> 00:38:26
because the horizontal velocity
is the same.

662
00:38:23 --> 00:38:29
That's independent of
whether there is gravity or not.

663
00:38:28 --> 00:38:34
There is no acceleration
in the x direction.

664
00:38:31 --> 00:38:37
And so they are both exactly
at the same x position.

665
00:38:36 --> 00:38:42

666
00:38:39 --> 00:38:45
What is this difference?

667
00:38:40 --> 00:38:46
Well, that is the difference

668
00:38:42 --> 00:38:48
between the equation with
gravity and without gravity.

669
00:38:46 --> 00:38:52
And y as a function of time--

670
00:38:51 --> 00:38:57
you can look at equation number
three there

671
00:38:54 --> 00:39:00
if you can still see it--

672
00:38:55 --> 00:39:01
equals v zero y, which is
v zero sine alpha time t

673
00:39:04 --> 00:39:10
minus one-half gt squared.

674
00:39:09 --> 00:39:15

675
00:39:13 --> 00:39:19
Well, if there is no gravity,
this term doesn't exist

676
00:39:19 --> 00:39:25
because that's
this straight line.

677
00:39:22 --> 00:39:28
(whooshes )

678
00:39:24 --> 00:39:30
With gravity,
it's the same thing

679
00:39:25 --> 00:39:31
but you have to subtract this.

680
00:39:28 --> 00:39:34
Therefore, this distance
is one-half g t1 squared.

681
00:39:35 --> 00:39:41
That is this distance

682
00:39:37 --> 00:39:43
so this curve is lower
by this amount.

683
00:39:42 --> 00:39:48
Now comes the time that
the golf ball hits point p.

684
00:39:48 --> 00:39:54
When its position is x t2
and the time here is t2

685
00:39:52 --> 00:39:58
that means if there
had been no gravity

686
00:39:55 --> 00:40:01
the golf ball
would have been there.

687
00:39:58 --> 00:40:04
They must have
the same position in x

688
00:40:01 --> 00:40:07
at this catastrophic moment.

689
00:40:03 --> 00:40:09
So what now is the distance

690
00:40:05 --> 00:40:11
between the monkey
and the golf ball--

691
00:40:08 --> 00:40:14
the distance
between the two trajectories--

692
00:40:12 --> 00:40:18
one trajectory, no gravity;
the other with gravity?

693
00:40:16 --> 00:40:22
This distance equals
one-half g t2 squared

694
00:40:21 --> 00:40:27
for that same reason.

695
00:40:24 --> 00:40:30
And we all know

696
00:40:26 --> 00:40:32
that if the monkey
at time t equals zero let go

697
00:40:31 --> 00:40:37
that in t2 seconds
it will have fallen

698
00:40:36 --> 00:40:42
exactly over a distance
one-half g t2 squared-- exactly.

699
00:40:42 --> 00:40:48
This couldn't be more tragic.

700
00:40:45 --> 00:40:51
And he will be killed.

701
00:40:46 --> 00:40:52

702
00:40:49 --> 00:40:55
You may say, "Well, yeah,
but you have manipulated

703
00:40:55 --> 00:41:01
the speed of that gun
just so nicely."

704
00:41:00 --> 00:41:06
Oh, no. Oh, no.

705
00:41:02 --> 00:41:08
I can shoot that with a higher
speed at the same angle alpha

706
00:41:07 --> 00:41:13
and the trajectory would be this

707
00:41:10 --> 00:41:16
and the monkey
would be killed there.

708
00:41:13 --> 00:41:19
I can do it with a lower speed

709
00:41:16 --> 00:41:22
and the monkey
would be killed here.

710
00:41:19 --> 00:41:25
It's independent
of the speed of the bullet

711
00:41:22 --> 00:41:28
because always this part here--
it's always exactly the distance

712
00:41:27 --> 00:41:33
that the monkey falls
in that time.

713
00:41:30 --> 00:41:36
However,
if the speed is very low--

714
00:41:32 --> 00:41:38
that it hits the ground before
the monkey hits the ground--

715
00:41:37 --> 00:41:43
well, okay,
then the monkey is safe.

716
00:41:40 --> 00:41:46
So the only thing that is very,
very critical is alpha.

717
00:41:45 --> 00:41:51
It must be precisely aimed
at the monkey.

718
00:41:49 --> 00:41:55
If that's not the case,
then the monkey will be safe.

719
00:41:55 --> 00:42:01
Now before we will witness this
classic and rather tragic drama,

720
00:42:00 --> 00:42:06
I want to look at this

721
00:42:01 --> 00:42:07
from a somewhat
different point of view

722
00:42:04 --> 00:42:10
namely from the point
of view of the monkey.

723
00:42:07 --> 00:42:13
The monkey sits there,
looks at the gun

724
00:42:11 --> 00:42:17
and the golf ball comes
to the monkey.

725
00:42:15 --> 00:42:21
And I will put them both in
a room which is an elevator

726
00:42:21 --> 00:42:27
and the elevator is in free fall

727
00:42:23 --> 00:42:29
and they don't even know that.

728
00:42:25 --> 00:42:31
They both fall
with the acceleration g.

729
00:42:28 --> 00:42:34

730
00:42:30 --> 00:42:36
Here is the monkey, free

731
00:42:35 --> 00:42:41
and here is the gun.

732
00:42:37 --> 00:42:43

733
00:42:41 --> 00:42:47
The velocity of that bullet
is v zero.

734
00:42:46 --> 00:42:52

735
00:42:50 --> 00:42:56
And so the monkey will see that
bullet come straight at him.

736
00:42:55 --> 00:43:01
There's no such thing as an arc.

737
00:42:58 --> 00:43:04
They both fall
in this falling grav...

738
00:43:01 --> 00:43:07
in this falling elevator.

739
00:43:03 --> 00:43:09
And so the bullet comes...

740
00:43:06 --> 00:43:12
(kisses )

741
00:43:07 --> 00:43:13
The monkey happens to be
a very intelligent monkey

742
00:43:11 --> 00:43:17
and the monkey says to himself,
"How long do I have to live?"

743
00:43:16 --> 00:43:22
And the monkey makes
the following calculation.

744
00:43:19 --> 00:43:25
(class laughs )

745
00:43:22 --> 00:43:28
LEWIN:
If this distance is d, and this
is h, then the monkey says

746
00:43:28 --> 00:43:34
"Aha, this is the square root
of d squared plus h squared."

747
00:43:33 --> 00:43:39
So from the monkey point
of view, the time for the kill

748
00:43:40 --> 00:43:46
will be the square root

749
00:43:43 --> 00:43:49
of d squared plus h squared
divided by v zero.

750
00:43:49 --> 00:43:55
That's how many seconds
he has to live.

751
00:43:51 --> 00:43:57

752
00:43:53 --> 00:43:59
Well, you people
are also quite smart

753
00:43:56 --> 00:44:02
and you look at this diagram
and you said, "No, no way."

754
00:44:01 --> 00:44:07
If this distance is D

755
00:44:04 --> 00:44:10
then the speed to reach this
point is v zero cosine alpha.

756
00:44:11 --> 00:44:17
In other words, the time
that it takes for this object

757
00:44:16 --> 00:44:22
to reach this value of x...

758
00:44:18 --> 00:44:24
So, for 26.100 MIT students

759
00:44:23 --> 00:44:29
t kill equals D divided
by v zero cosine alpha.

760
00:44:31 --> 00:44:37
But what is the cosine of alpha?

761
00:44:36 --> 00:44:42
That is D divided
by the square root

762
00:44:40 --> 00:44:46
of D squared plus h squared.

763
00:44:43 --> 00:44:49
So I can replace
this cosine alpha

764
00:44:47 --> 00:44:53
by D divided by the square root.

765
00:44:52 --> 00:44:58
So I can replace
this cosine alpha

766
00:44:55 --> 00:45:01
by D divided by the square root.

767
00:44:57 --> 00:45:03

768
00:45:01 --> 00:45:07
And you and the monkey
agree exactly

769
00:45:04 --> 00:45:10
on the amount of time
that the monkey has to live.

770
00:45:08 --> 00:45:14
It better be that way,
because this could not depend

771
00:45:13 --> 00:45:19
on which reference frame
you work in--

772
00:45:17 --> 00:45:23
the falling reference frame

773
00:45:19 --> 00:45:25
or, for that matter
the reference frame of 26.100.

774
00:45:24 --> 00:45:30
The monkey will be placed

775
00:45:26 --> 00:45:32
at about three meters
above the table.

776
00:45:29 --> 00:45:35
We all know that it takes
about 0.8 seconds.

777
00:45:32 --> 00:45:38
We have done many experiments
at three meters.

778
00:45:35 --> 00:45:41
It takes about 0.8 seconds.

779
00:45:37 --> 00:45:43
So the whole thing
will go very fast.

780
00:45:39 --> 00:45:45
We are going to put
a monkey up there.

781
00:45:41 --> 00:45:47

782
00:45:44 --> 00:45:50
I want you to first see
the trajectory of that golf ball

783
00:45:48 --> 00:45:54
before we bring the monkey in.

784
00:45:50 --> 00:45:56
It is already so painful
for this monkey.

785
00:45:52 --> 00:45:58
You don't want him
to pre-experience

786
00:45:55 --> 00:46:01
what's going to happen.

787
00:45:56 --> 00:46:02
So we will do this
in the absence of the monkey

788
00:46:02 --> 00:46:08
and we will let you...
I will let you see

789
00:46:06 --> 00:46:12
what roughly the trajectory
of that bullet will be.

790
00:46:12 --> 00:46:18
Three, two, one, zero.

791
00:46:15 --> 00:46:21
(gun claps )

792
00:46:16 --> 00:46:22
(ball bouncing )

793
00:46:18 --> 00:46:24
So it will hit somewhere here.

794
00:46:20 --> 00:46:26
That's that point p.

795
00:46:22 --> 00:46:28
So when you're going to see
the drama in action

796
00:46:26 --> 00:46:32
this is where
the monkey will reach

797
00:46:28 --> 00:46:34
when the two hit each other.

798
00:46:31 --> 00:46:37

799
00:46:34 --> 00:46:40
Now you can imagine that this

800
00:46:37 --> 00:46:43
is a very painful day
for the monkey.

801
00:46:40 --> 00:46:46
And I'm going to get the monkey.

802
00:46:43 --> 00:46:49
It's behind here

803
00:46:45 --> 00:46:51
and I hope that you would pay
some respect to Robert.

804
00:46:50 --> 00:46:56
His name is Robert,
and it may take me a minute.

805
00:46:54 --> 00:47:00

806
00:46:57 --> 00:47:03
(class murmurs )

807
00:46:59 --> 00:47:05

808
00:47:39 --> 00:47:45
(class cheers and laughs )

809
00:47:42 --> 00:47:48
LEWIN:
Here is Robert.

810
00:47:44 --> 00:47:50
(laughter continues )

811
00:47:47 --> 00:47:53

812
00:47:49 --> 00:47:55
I thought...

813
00:47:51 --> 00:47:57
(class applauds )

814
00:47:54 --> 00:48:00

815
00:47:56 --> 00:48:02
LEWIN:
I thought it was appropriate
to change for the occasion.

816
00:48:01 --> 00:48:07
I don't go on monkey hunts
too often

817
00:48:04 --> 00:48:10
but when I do it,
I'd like to do it in style.

818
00:48:08 --> 00:48:14
(class laughs )

819
00:48:12 --> 00:48:18

820
00:48:14 --> 00:48:20
Here is Robert, and we're going
to put Robert up here.

821
00:48:21 --> 00:48:27
Robert has in his head
a metal plate...

822
00:48:26 --> 00:48:32

823
00:48:31 --> 00:48:37
so that when we activate
the electromagnet

824
00:48:36 --> 00:48:42
that we can stick him on there
 

825
00:48:39 --> 00:48:45
and when we take the current
off, then Robert will fall.

826
00:48:45 --> 00:48:51
So this is the activation
of the electromagnet.

827
00:48:48 --> 00:48:54

828
00:48:55 --> 00:49:01
So here we go.

829
00:48:57 --> 00:49:03
I can see Robert is nervous.

830
00:48:59 --> 00:49:05
(class laughs )

831
00:49:01 --> 00:49:07
And you can't blame him.

832
00:49:03 --> 00:49:09
This is not the greatest day
of his life.

833
00:49:06 --> 00:49:12
(class laughs )

834
00:49:08 --> 00:49:14
Oh, by the way,
I want you to know

835
00:49:10 --> 00:49:16
we are not cruel here.

836
00:49:12 --> 00:49:18
He's wearing
a bulletproof vest.

837
00:49:15 --> 00:49:21
(class laughs )

838
00:49:20 --> 00:49:26
Oh, boy, I can... I can feel
him shaking all over his body.

839
00:49:24 --> 00:49:30
He's very nervous.

840
00:49:25 --> 00:49:31

841
00:49:27 --> 00:49:33
Robert, don't let go yet!

842
00:49:30 --> 00:49:36
Oh, let me show you.

843
00:49:32 --> 00:49:38
It's important that you know

844
00:49:35 --> 00:49:41
that we have done
everything we can

845
00:49:38 --> 00:49:44
to aim this gun as accurately
as we can at Robert.

846
00:49:43 --> 00:49:49

847
00:49:53 --> 00:49:59
Robert, don't let go yet.

848
00:49:56 --> 00:50:02

849
00:49:58 --> 00:50:04
We've got to first cock the gun.

850
00:50:00 --> 00:50:06
Hold it, now, hold it, Robert!

851
00:50:02 --> 00:50:08
(class laughs )

852
00:50:06 --> 00:50:12
This happens always with Robert.

853
00:50:08 --> 00:50:14
(laughter )

854
00:50:10 --> 00:50:16

855
00:50:13 --> 00:50:19
(Lewin admonishes Robert
in whispers )

856
00:50:16 --> 00:50:22
(class laughs )

857
00:50:17 --> 00:50:23

858
00:50:28 --> 00:50:34
Okay, he just promised me
that he will not let go again.

859
00:50:33 --> 00:50:39

860
00:50:44 --> 00:50:50
When I cock the gun-- if I can
find the golf ball, it's here--

861
00:50:53 --> 00:50:59
then the electric circuit
takes over
 

862
00:50:58 --> 00:51:04
and now the current
will be disconnected

863
00:51:03 --> 00:51:09
when the gun is fired.

864
00:51:05 --> 00:51:11

865
00:51:09 --> 00:51:15
Even I... even I'm nervous.

866
00:51:11 --> 00:51:17
I admit it, you know,
this is a terrible thing to do.

867
00:51:13 --> 00:51:19

868
00:51:15 --> 00:51:21
Terrible thing to do.

869
00:51:19 --> 00:51:25
(sighs )

870
00:51:20 --> 00:51:26
You ready?

871
00:51:21 --> 00:51:27
Three, two, one, zero.

872
00:51:25 --> 00:51:31
(gun clicks )

873
00:51:26 --> 00:51:32
(class exclaims )

874
00:51:28 --> 00:51:34
(loud echo reverberates )

875
00:51:30 --> 00:51:36

876
00:51:45 --> 00:51:51
LEWIN:
Poor monkey.

877
00:51:47 --> 00:51:53

878
00:51:52 --> 00:51:58
See you Friday.

879
00:51:53 --> 00:51:59.000