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## Elastic collisions and conservation of momentum

Current time:0:00Total duration:6:00

# Momentum: Ice skater throws a ball

## Video transcript

Welcome back. I'll now do a couple of more
momentum problems. So this first problem, I have
this ice skater and she's on an ice skating rink. And what she's doing is
she's holding a ball. And this ball-- let me draw
the ball-- this is a 0.15 kilogram ball. And she throws it. Let's just say she throws it
directly straight forward in front of her, although
she's staring at us. She's actually forward
for her body. So she throws it exactly
straight forward. And I understand it is hard to
throw something straight forward, but let's assume
that she can. So she throws it exactly
straight forward with a speed-- or since we're going to
give the direction as well, it's a velocity, right, cause
speed is just a magnitude while a velocity is a magnitude
and a direction-- so she throws the ball at 35 meters
per second, and this ball is 0.15 kilograms. Now, what the problem says is
that their combined mass, her plus the ball, is 50 kilograms.
So they're both stationary before she does
anything, and then she throws this ball, and the question is,
after throwing this ball, what is her recoil velocity? Or essentially, well how much,
by throwing the ball, does she push herself backwards? So what is her velocity in
the backward direction? And if you're not familiar with
the term recoil, it's often applied to when someone,
I guess, not that we want to think about violent things, but
if you shoot a gun, your shoulder recoils back,
because once again momentum is conserved. So there's a certain amount of
momentum going into that bullet, which is very light
and fast going forward. But since momentum is conserved,
your shoulder has velocity backwards. But we'll do another
problem with that. So let's get back
to this problem. So like I just said, momentum
is conserved. So what's the momentum at the
start of the problem, the initial momentum? Let me do a different color. So this is the initial
momentum. Initially, the mass is 50
kilograms, right, cause her and the ball combined are 50
kilograms, times the velocity. Well the velocity is 0. So initially, there is 0
velocity in the system. So the momentum is 0. The P initial is equal to 0. And since we start with a net 0
momentum, we have to finish with a net 0 momentum. So what's momentum later? Well we have a ball moving at
35 meters per second and the ball has a mass of 0.15
kilograms. I'll ignore the units for now just
to save space. Times the velocity
of the ball. Times 35 meters per second. So this is the momentum of the
ball plus the new momentum of the figure skater. So what's her mass? Well her mass is going
to be 50 minus this. It actually won't matter a ton,
but let's say it's 49-- what is that-- 49.85 kilograms, times her new velocity. Times velocity. Let's call that the velocity
of the skater. So let me get my trusty
calculator out. OK, so let's see. 0.15 times 35 is
equal to 5.25. So that equals 5.25. plus 49.85 times the skater's
velocity, the final velocity. And of course, this equals
0 because the initial velocity was 0. So let's, I don't know, subtract
5.25 from both sides and then the equation becomes
minus 5.25 is equal to 49.85 times the velocity
of the skater. So we're essentially saying that
the momentum of just the ball is 5.25. And since the combined system
has to have 0 net momentum, we're saying that the momentum
of the skater has to be 5.25 in the other direction, going
backwards, or has a momentum of minus 5.25. And to figure out the velocity,
we just divide her momentum by her mass. And so divide both sides by
49.85 and you get the velocity of the skater. So let's see. Let's make this a negative
number divided by 49.85 equals minus 0.105. So minus 0.105 meters
per second. So that's interesting. When she throws this ball out at
35 meters per second, which is pretty fast, she will
recoil back at about 10 centimeters, yeah, roughly 10
centimeters per second. So she will recoil a lot
slower, although she will move back. And if you think about it, this
is a form of propulsion. This is how rockets work. They eject something that maybe
has less mass, but super fast. And that, since we have a
conservation of momentum, it makes the rocket move in
the other direction. Well anyway, let's see if we
could fit another problem in. Actually, it's probably better
to leave this problem done and then I'll have more time for the
next problem, which will be slightly more difficult. See you soon.

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