Finding Velocity(Momentum related)

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AI Thread Summary
The discussion revolves around a physics problem involving two balls, where a small ball is dropped onto a larger ball that is also falling. The key point is that the large ball's rebound velocity after an elastic collision with the floor affects the small ball's velocity upon collision, resulting in the small ball rebounding at three times its initial velocity. Participants express confusion about how to approach the problem without specific mass values and seek guidance on applying conservation of momentum and energy principles. The correct approach involves using the equations for momentum and energy conservation to derive the small ball's rebound characteristics. Understanding these concepts is crucial for solving the problem effectively.
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Homework Statement


Suppose you hold a small ball in contact with, and directly over, the center of a large ball. If you then drop the small ball a short time after dropping the large ball, the small ball rebounds with surprising speed. To show the extreme case, ignore air resistance and suppose the large ball makes an elastic collision with the floor and then rebounds to make an elastic collision with the still-descending small ball. Just before the collision between the two balls, the large ball is moving upward with velocity and the small ball has velocity . (Do you see why?) Assume the large ball has a much greater mass than the small ball.

(a) What is the velocity of the small ball immediately after its collision with the large ball? (answer is V_B = 3V_b)

(b) From the answer to part (a), what is the ratio of the small ball's rebound distance to the distance it fell before the collision?

Homework Equations


m1v1=m2v2

The Attempt at a Solution



I'm really not sure how to start this out. Our professor gave us this answer to the first part of the problem but I'm not see how I can come to that conclusion. I'm really having an issue with there just being "large and small" masses and not specific values. How do I go about progressing in this problem? Thanks.

EDIT: I was told to find the consvervation of momentum and then find the conservation of energy to find the velocity of the smaller ball. So I would do MaVa = MbVb, solve for Va. Not sure how conservation of energy will be. Will it just be KEa + GPEa = KEb + GPEb?
 
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