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Inspired by
Daryn's post in
this awesome thread:
This is a popular question in freshman physics. Imagine this set-up (because I don't want to take the time to MS Paint it): You have a wall at the front end of a cart and you're standing on the back end of this cart facing the wall and you have a bunch of perfectly elastic tennis balls. You throw the balls against the wall and they bounce off. Describe the motion of the cart, assuming perfect bearings and a smooth, no-slip condition between the flat ground and the wheels.
If you can't figure out what I'm talking about, imagine Daryn's fan on skateboard picture and replace the fan with a little person throwing tennis balls against the "sail".
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I assume you mean the wall never deforms, there is no friction or drag of the cart apparatus interacting with the ground, etc. such that this is a pure first-approximation problem.
Further assume the ball thrower both throws and catches the ball accurately every time, and that he throws such that the ball hits level with his throw.
In that case, the cart herky-jerks but the net is it moves forward - quite quickly after enough throws, unless you assume there is no air resistance, in which case it herky-jerks but does not move.
Bonus question: Does gravity affect the motion of the described ball-and-cart?