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Welcome back.

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I'll now do a couple of more
momentum problems.

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So this first problem, I have
this ice skater and she's on

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an ice skating rink.

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And what she's doing is
she's holding a ball.

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And this ball-- let me draw
the ball-- this is a 0.15

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kilogram ball.

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And she throws it.

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Let's just say she throws it
directly straight forward in

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front of her, although
she's staring at us.

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She's actually forward
for her body.

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So she throws it exactly
straight forward.

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And I understand it is hard to
throw something straight

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forward, but let's assume
that she can.

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So she throws it exactly
straight forward with a

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speed-- or since we're going to
give the direction as well,

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it's a velocity, right, cause
speed is just a magnitude

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while a velocity is a magnitude
and a direction-- so

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she throws the ball at 35 meters
per second, and this

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ball is 0.15 kilograms.

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Now, what the problem says is
that their combined mass, her

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plus the ball, is 50 kilograms.
So they're both

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stationary before she does
anything, and then she throws

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this ball, and the question is,
after throwing this ball,

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what is her recoil velocity?

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Or essentially, well how much,
by throwing the ball, does she

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push herself backwards?

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So what is her velocity in
the backward direction?

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And if you're not familiar with
the term recoil, it's

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often applied to when someone,
I guess, not that we want to

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think about violent things, but
if you shoot a gun, your

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shoulder recoils back,
because once

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again momentum is conserved.

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So there's a certain amount of
momentum going into that

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bullet, which is very light
and fast going forward.

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But since momentum is conserved,
your shoulder has

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velocity backwards.

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But we'll do another
problem with that.

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So let's get back
to this problem.

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So like I just said, momentum
is conserved.

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So what's the momentum at the
start of the problem, the

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initial momentum?

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Let me do a different color.

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So this is the initial
momentum.

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Initially, the mass is 50
kilograms, right, cause her

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and the ball combined are 50
kilograms, times the velocity.

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Well the velocity is 0.

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So initially, there is 0
velocity in the system.

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So the momentum is 0.

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The P initial is equal to 0.

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And since we start with a net 0
momentum, we have to finish

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with a net 0 momentum.

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So what's momentum later?

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Well we have a ball moving at
35 meters per second and the

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ball has a mass of 0.15
kilograms. I'll ignore the

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units for now just
to save space.

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Times the velocity
of the ball.

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Times 35 meters per second.

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So this is the momentum of the
ball plus the new momentum of

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the figure skater.

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So what's her mass?

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Well her mass is going
to be 50 minus this.

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It actually won't matter a ton,
but let's say it's 49--

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what is that-- 49.85 kilograms,

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times her new velocity.

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Times velocity.

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Let's call that the velocity
of the skater.

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So let me get my trusty
calculator out.

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OK, so let's see.

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0.15 times 35 is
equal to 5.25.

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So that equals 5.25.

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plus 49.85 times the skater's
velocity, the final velocity.

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And of course, this equals
0 because the initial

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velocity was 0.

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So let's, I don't know, subtract
5.25 from both sides

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and then the equation becomes
minus 5.25 is equal to 49.85

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times the velocity
of the skater.

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So we're essentially saying that
the momentum of just the

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ball is 5.25.

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And since the combined system
has to have 0 net momentum,

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we're saying that the momentum
of the skater has to be 5.25

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in the other direction, going
backwards, or has a momentum

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of minus 5.25.

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And to figure out the velocity,
we just divide her

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momentum by her mass.

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And so divide both sides by
49.85 and you get the velocity

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of the skater.

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So let's see.

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Let's make this a negative
number divided by 49.85 equals

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minus 0.105.

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So minus 0.105 meters
per second.

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So that's interesting.

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When she throws this ball out at
35 meters per second, which

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is pretty fast, she will
recoil back at about 10

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centimeters, yeah, roughly 10
centimeters per second.

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So she will recoil a lot
slower, although

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she will move back.

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And if you think about it, this
is a form of propulsion.

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This is how rockets work.

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They eject something that maybe
has less mass, but super

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fast. And that, since we have a
conservation of momentum, it

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makes the rocket move in
the other direction.

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Well anyway, let's see if we
could fit another problem in.

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Actually, it's probably better
to leave this problem done and

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then I'll have more time for the
next problem, which will

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be slightly more difficult.

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See you soon.

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