A ball is held at rest at some height above a hard, horizontal surface. Once the...

A ball is held at rest at some height above a hard, horizontal surface. Once the ball is released it falls, hits the surface, and starts bouncing vertically up and down. Suppose that with each bounce the ball loses a fixed fraction p (with 1>p>0) of its energy. This loss could be due to a number of reasons (inelasticity, drag, etc) that are left unspecified.

How many times will the ball bounce before coming to rest (if at all)? Provide a detailed explanation of your reasoning, not simply a one-line answer.
How long will it take for the ball to come to rest (if at all)? Give your answer as a formula that contains as variables only p and the time T₁ from the moment that the ball was released to the first contact with the horizontal surface.

Answer should contain careful and detailed reasoning

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Expert Solution

genius_generous answered 1 month ago

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