WEBVTT

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For one-dimensional collisions,
let's talk about two objects, 1

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and object 2, moving with
velocity V1 and another object

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V2 moving with velocity V2.

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Let's say they're
moving on the ground.

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Now I'd like to introduce the
concept of relative velocity,

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a concept that we experience
all the time in our lives.

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But let's see what
it actually means.

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So V relative, I'm
going to define

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this to be the velocity of
V1 minus the velocity of V2.

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Now because of this minus
sign that seems a little bit

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about abstract.

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But one typical example where
we see this all the time

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is for people
traveling on highways.

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You might have two cars, one
car overtaking the other car.

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But if you're
sitting in car 1, it

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looks like car 2 is
going quite slow.

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So let's just take
typical highway example.

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So you might have V1.

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And we'll give it some speed.

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So we'll make it
60 miles per hour.

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And we'll just call this
one-dimensional problem i hat.

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And V2-- notice
we're not speeding

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on a highway-- V2 is going
at 50 miles per hour,

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i hat, very slow.

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And the relative velocity,
V1 minus V2-- so that's

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what we're calling V relative--
that's 60 miles per hour

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minus 50 miles per hour i hat.

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And that's just
10 miles per hour.

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And that's what people
experience when one car is

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approaching another car.

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If you're in car 2, car
1 seems like it's coming

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at you at 10 miles per hour.

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This is what we mean
by relative velocity.

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There's another
important example--

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so that's example 1-- the other
important example to look at,

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example 2, is when
two objects are

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moving in opposite directions.

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So let's just see write them in
terms of components this time.

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So we have V2 x1.

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And we have V2.

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And let's make V1 x positive.

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So object 1 is moving
in that direction.

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And let's write
this one as V2 x.

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We don't have to
call this initial.

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We'll just call it V2 x i hat.

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And here V2 x is
equal to minus V1 x.

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So its component is negative.

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And even though we drew
an arrow in this picture,

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the picture is still fine,
because if the component is

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negative, it means it's moving
in the opposite direction.

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The key arrow is the unit vector
when we are writing components.

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And now V relative in this case
is V1 x i hat minus V2 x i hat.

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That's the V1 x i
hat minus minus.

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So there's another V1 x i hat.

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So the relative
velocity in this case

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has a component that's
twice the speed of V1.

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If two objects are moving
together at the same speed,

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the relative velocity,
the way we've defined it,

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has twice the magnitude
of either velocity.

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And this is an important example
to consider in collisions.

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Now this relative velocity
concept we'll see we'll

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add a new way of thinking
about elastic collisions

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with no external forces
in one dimension.