Two boys are standing on carts that move along a horizontal frictionless surface

Question

Two boys are standing on carts that move along a horizontal frictionless surface. The
mass of each boy-cart combination is 100 kg, and each moves initially with the velocities
shown above. The boy on cart A decides to throw a 2 kg ball to the boy on cart B
(assume the ball travels horizontally). The boy on cart B then throws the ball at 15 m/sec
in the forward direction and finds, surprisingly, that his cart has come completely to rest.
At what speed must the boy on cart A have thrown the ball in order to make this happen?

Explanation / Answer

By momentum conservation this can be solved:

Every time momentum of different systems are constant:

Final momentum of (ball + B) = Initial momentum of ball coming + Initial momentum of Bbefore receiving the ball

0 + 2*15 = 100*0.1 + 2*v(ball)

=> 30 = 10 + 2v => v = 10m/s

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