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We will practice going
between reference frames

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to look at relative
velocities in one dimension.

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Let's say that an observer
is standing on the sidewalk

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and that observer
sees a car drive

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past to the right
at a speed of v car.

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The observer also
sees a bike that's

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riding to the left at
a slower speed, v bike.

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Now, I'm interested
in what the car looks

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like from the
perspective of the bike.

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The bike sees
itself as stationary

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and sees the world around
it moving to the right.

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To the bike, the
observer on the sidewalk

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appears to be moving to the
right with the speed of v bike.

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The car was moving to the
right relative to the reference

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frame of the observer
standing on the sidewalk.

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So to the bike, the
car looks like it's

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going even faster to the
right with a total speed

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of v car plus v bike.

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Let's say, later on the
biker throws an apple

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in the direction of her movement
and sees this apple travel

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to the left with the
speed of v apple.

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Now I want to know
what an observer sees

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in the stationary
frame on the sidewalk.

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The apple appears to
be traveling a speed v

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apple faster than the
biker all to the left.

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So the observer on the sidewalk
will see the apple move

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to the left with a total
speed of v apple plus v bike.

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Now let's say the person
throws the apple forward

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at a speed v apple.

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What does the car see?

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To the car the apple is going
to the left at the speed of v

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car minus v apple.

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How about the bike?

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To the bike, the apple is going
at a speed of v apple plus v

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bike to the right.