Math M131A

a rubber ball has the property that on any bounce it returns to 1/3 of the height from which it just fell. Suppose the ball is dropped from 108 ft How far has the ball traveled by the fourth bounce?

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  1. end of first bounce it dropped 108 ft
    during the second bounce it went up and down
    (1/3) of 108 or 2(1/3)(108) = 72
    during the third bounce it went
    2(1/3)(72) = 48
    during the fourth bounce it went
    2(1/3)(48) = 32

    so after 4 bounces it went
    108+72+48+32 = 260

    make a sketch, label the bounces and see why I only took half of the first bounce cylcle

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