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Math Help - Series problem. Cant seem to get this one.

  1. #1
    Junior Member
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    Series problem. Cant seem to get this one.

    Thanks for any help

    A ball drops from a height of 13 feet. Each time it hits the ground, it bounces up 70 percents of the height it fall. Assume it goes on forever, find the total distance it travels.
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hello

    Let's call d_k the distance (in feet) that the ball travels between the k-th and (k+1)-th bounce.
    What is d_0 ? d_1 ? d_2 ? d_{k+1} in function of d_k ? d_k in function of k ?
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  3. #3
    Eater of Worlds
    galactus's Avatar
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    This is a classic geometric series.

    Each is 70% of the previous.

    Downward the ball travels 13+9.1+6.37+4.459+.........

    Upward the ball travels 9.1+6.37+4.459+..............

    We can assume the total distance the ball travels, S, can be found by adding the infinite series.

    S=13+2(9.1+6.37+4.459+...........)

    =13+2\left[9.1+9.1(.7)+9.1(.7)^{2}+9.1(.7)^{3}+..........\rig  ht]

    Now we can use the formula S=\frac{a_{1}}{1-r}

    Where a_{1}=9.1, \;\ r=.7

    S=13+2\left[\frac{9.1}{1-.7}\right]=73.6667
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