Math

When dropped on a hard surface, a rubber ball takes a series of bounces, each one about 4/5 as high as the preceding one. If the rubber ball is dropped from a height of 20 ft, what is the approximate distance the ball travels before coming to rest? Please explain how you got the answer. Thanks!

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  1. assume an infinite number of hops. In practice, of course, the ball stops earlier than that, but you have a geometric progression where

    a = 20
    r = 4/5

    So, the initial drop is 20, and each bounce is a round trip 4/5 as high as the one before, so the total distance after n hops is

    20 + 2(20 * 4/5) + 2(20*4/5)^2 + ...

    So, the real GP is

    a = 40
    r = 4/5
    and 20 must be subtracted because the first hop did not have to go up.

    The total distance is thus

    40/(1 - 4/5) - 20 = 180 ft

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  2. Thank you so much!

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