Here\'s another one with that cart with the tennis balls. This time, we\'re goin
ID: 1837357 • Letter: H
Question
Here's another one with that cart with the tennis balls. This time, we're going to compare two different situations: one where you are launching the tennis balls off the back end of the cart with velocity v0, and the other where tennis balls are being thrown onto your cart at velocity u0 by your friend (who is not on the cart). The question is, starting from rest n both cases, which cart will reach a greater speed, after a whole bunch of throws? Let's imagine some scenario where the friend who is not on the cart can somehow keep up with the cart, and throw perfectly, etc.... I hope to see clear, sensible arguments for both answers, and a clear, sensible reason for why the one you think is wrong is wrong.Explanation / Answer
When launched from Cart:
momentum of cart-person-ball system will be conserved.
Applying,
0 = mv0 + (M)v
where m = mass of ball
M = mass of cart plus person
v = - mv0/M
so cart will move with speed mv0/M in opposite direction.
When launched by friend ffrom outside:
Applying momentum conservation,
M*0 + m v0 = (M +m)v1
after catching whole system will move with speed v together.
v1 = mv0 / (M + m)
As we can see M+m > m
hence v1 < v
so cart will movefaster when ball is launched from cart.