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So we've been trying to find
the velocity of the cart

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and the velocity of
the person in terms

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of the relative
velocity of the person

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jumping in the reference
frame of the moving cart,

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the mass of the person,
and the mass of the cart.

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We've already solved
this in the ground frame,

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now I would like to solve this
in which my reference frame is

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the moving frame.

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So our pictures in
the moving frame

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were actually much easier.

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Because the moving
frame is traveling

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with the final
speed of the cart,

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at the final interaction--
after the interaction is

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done-- in this moving
frame, the cart is at rest.

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They're moving together.

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You're sitting in the cart.

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You're moving at the same speed.

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The person jumped off with
speed u relative to the cart.

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The tricky part was to
realize that, in the ground

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frame-- when the cart is at
rest here in the ground frame--

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an observer moving
with speed Vc would

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see the person in the cart
moving backwards in the moving

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train with a speed minus Vc.

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So now we can apply the momentum
principle to these two states.

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In the moving frame,
we have that momentum

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of the system initially equals
the momentum of the system

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finally.

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Now, the initial momentum is
just minus Mp plus M cart V

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cart-- notice the minus V cart.

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And the final momentum is
equal to just M person u.

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And so we see that V cart
equals minus M person

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u over M person plus
Mc, which is exactly

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the same result that we
got in the ground frame

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but it was actually much easier
to solve in the moving frame.