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On 2017/Feb/23, at 08:41, Jeffrey Schnick <JSchnick@Anselm.Edu> wrote:
A student came to me with a practice problem from a math class involving the old tennis ball on basketball demo. The goal was to find the max height above the floor achieved by the tennis ball after the two were dropped from a given height with the tennis ball on top of and in contact with the basketball on the way down. It is clear we have to look up information on the masses and coefficients of restitution or make some assumptions. Suppose we assume that both interactions are perfectly elastic. I looked up a solution on the internet where it was claimed that you could treat the process as if the basketball bounced off the floor and was on its way up by the time it collided with the tennis ball which at that time would still be on its way down.
<https://www.physics.harvard.edu/uploads/files/undergrad/probweek/sol1.pdf >
This suggests that the timing doesn’t matter. It seems to me that the timing does matter. For instance, if the tennis ball comes off the basketball at the instant the basketball, while in contact with the floor, arrives at a velocity of zero, the tennis ball would leave the basketball with about the same speed it would have just after hitting the floor after having fallen the same distance and so it would go about as high as if you dropped it on the floor by itself from the same height. To me it seems like a more complicated problem than the solution referenced above would suggest. Can you justify their claim about the timing? Any insights would be appreciated.
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