1
00:00:04,300 --> 00:00:08,440
For one-dimensional collisions,
let's talk about two objects, 1

2
00:00:08,440 --> 00:00:14,170
and object 2, moving with
velocity V1 and another object

3
00:00:14,170 --> 00:00:17,046
V2 moving with velocity V2.

4
00:00:17,046 --> 00:00:18,670
Let's say they're
moving on the ground.

5
00:00:18,670 --> 00:00:21,790
Now I'd like to introduce the
concept of relative velocity,

6
00:00:21,790 --> 00:00:24,940
a concept that we experience
all the time in our lives.

7
00:00:24,940 --> 00:00:27,250
But let's see what
it actually means.

8
00:00:27,250 --> 00:00:30,370
So V relative, I'm
going to define

9
00:00:30,370 --> 00:00:35,730
this to be the velocity of
V1 minus the velocity of V2.

10
00:00:35,730 --> 00:00:38,500
Now because of this minus
sign that seems a little bit

11
00:00:38,500 --> 00:00:39,920
about abstract.

12
00:00:39,920 --> 00:00:43,250
But one typical example where
we see this all the time

13
00:00:43,250 --> 00:00:45,640
is for people
traveling on highways.

14
00:00:45,640 --> 00:00:49,300
You might have two cars, one
car overtaking the other car.

15
00:00:49,300 --> 00:00:51,580
But if you're
sitting in car 1, it

16
00:00:51,580 --> 00:00:54,580
looks like car 2 is
going quite slow.

17
00:00:54,580 --> 00:00:57,460
So let's just take
typical highway example.

18
00:00:57,460 --> 00:00:59,590
So you might have V1.

19
00:00:59,590 --> 00:01:00,970
And we'll give it some speed.

20
00:01:00,970 --> 00:01:03,910
So we'll make it
60 miles per hour.

21
00:01:03,910 --> 00:01:08,350
And we'll just call this
one-dimensional problem i hat.

22
00:01:08,350 --> 00:01:11,410
And V2-- notice
we're not speeding

23
00:01:11,410 --> 00:01:15,789
on a highway-- V2 is going
at 50 miles per hour,

24
00:01:15,789 --> 00:01:18,580
i hat, very slow.

25
00:01:18,580 --> 00:01:22,690
And the relative velocity,
V1 minus V2-- so that's

26
00:01:22,690 --> 00:01:28,990
what we're calling V relative--
that's 60 miles per hour

27
00:01:28,990 --> 00:01:32,830
minus 50 miles per hour i hat.

28
00:01:32,830 --> 00:01:34,490
And that's just
10 miles per hour.

29
00:01:34,490 --> 00:01:37,539
And that's what people
experience when one car is

30
00:01:37,539 --> 00:01:40,450
approaching another car.

31
00:01:40,450 --> 00:01:43,539
If you're in car 2, car
1 seems like it's coming

32
00:01:43,539 --> 00:01:45,560
at you at 10 miles per hour.

33
00:01:45,560 --> 00:01:47,710
This is what we mean
by relative velocity.

34
00:01:47,710 --> 00:01:49,720
There's another
important example--

35
00:01:49,720 --> 00:01:55,030
so that's example 1-- the other
important example to look at,

36
00:01:55,030 --> 00:01:58,240
example 2, is when
two objects are

37
00:01:58,240 --> 00:02:01,370
moving in opposite directions.

38
00:02:01,370 --> 00:02:07,810
So let's just see write them in
terms of components this time.

39
00:02:07,810 --> 00:02:09,699
So we have V2 x1.

40
00:02:09,699 --> 00:02:11,830
And we have V2.

41
00:02:11,830 --> 00:02:14,620
And let's make V1 x positive.

42
00:02:14,620 --> 00:02:17,950
So object 1 is moving
in that direction.

43
00:02:17,950 --> 00:02:21,370
And let's write
this one as V2 x.

44
00:02:21,370 --> 00:02:23,760
We don't have to
call this initial.

45
00:02:23,760 --> 00:02:27,740
We'll just call it V2 x i hat.

46
00:02:27,740 --> 00:02:33,220
And here V2 x is
equal to minus V1 x.

47
00:02:33,220 --> 00:02:36,160
So its component is negative.

48
00:02:36,160 --> 00:02:38,620
And even though we drew
an arrow in this picture,

49
00:02:38,620 --> 00:02:40,870
the picture is still fine,
because if the component is

50
00:02:40,870 --> 00:02:44,260
negative, it means it's moving
in the opposite direction.

51
00:02:44,260 --> 00:02:49,000
The key arrow is the unit vector
when we are writing components.

52
00:02:49,000 --> 00:02:57,880
And now V relative in this case
is V1 x i hat minus V2 x i hat.

53
00:02:57,880 --> 00:03:01,750
That's the V1 x i
hat minus minus.

54
00:03:01,750 --> 00:03:05,320
So there's another V1 x i hat.

55
00:03:05,320 --> 00:03:08,560
So the relative
velocity in this case

56
00:03:08,560 --> 00:03:12,520
has a component that's
twice the speed of V1.

57
00:03:12,520 --> 00:03:16,210
If two objects are moving
together at the same speed,

58
00:03:16,210 --> 00:03:18,820
the relative velocity,
the way we've defined it,

59
00:03:18,820 --> 00:03:23,030
has twice the magnitude
of either velocity.

60
00:03:23,030 --> 00:03:27,020
And this is an important example
to consider in collisions.

61
00:03:27,020 --> 00:03:30,850
Now this relative velocity
concept we'll see we'll

62
00:03:30,850 --> 00:03:35,560
add a new way of thinking
about elastic collisions

63
00:03:35,560 --> 00:03:39,090
with no external forces
in one dimension.