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

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Physics

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

  1. How many times will the ball bounce before coming to rest (ifat all)? Provide a detailed explanation of your reasoning, notsimply a one-line answer.
  2. 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 andthe time T1 from the moment that the ball was releasedto the first contact with the horizontal surface.

Answer should contain careful and detailed reasoning

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