math

A ball is dropped from a height of 18 m.On each rebound it rises 2/3 of the height from which it last fell. What distance has it travelled at the instant it strikes the ground for the 5th time?

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  1. first strike -- 18 m
    2nd strike -- 2(2/3)(18) = (4/3)(18)
    3rd strike -- 2(2/3)^2 (18) = 8/9 (18)
    4th strike -- 2(2/3)^3 (18) = 16/27 (18)
    5th strike -- 2(2/3)^4 (18) = 32/81 (18)

    total = 18 + 4 terms of the GP, with a = 72/3 , r = 2/3, n = 4

    sum = 18 + (72/3)((1 - 2/3)^4 )/(1 - 2/3)
    = appr 75.78 m

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