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Unformatted text preview: Let us assume that the ball is not dropped, but propelled upward to the first height h . This makes t = 2 2 h g . Thus the length of time that the ball bounces is given by the following. T = 2 e n 2 h g n = ! " = 2 2 h g # e n n = ! " = 2 2 h g # 1 1 $ e Let us now make some calculations using our formula. Suppose that h = 3_ ft and that e = .8 . Then T = 4.3184 _ s . If h = 10_ ft and that e = .99 , then T = 157.686 _ s . If h = 10_ ft and that e = .9999 , then T = 15768.6 _ s . In the last case the ball bounces 4.38016 hours. If e = 1 , then the impact is perfectly elastic and the ball will bounce forever. This is an application of the geometric series. Below is a graph of a few bounces for e = 2 3 . The second graph is for e = 9 10 ....
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- Spring '08