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Math Help - how high was the ball dropped?

  1. #1
    rcs
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    how high was the ball dropped?

    Can anybody help me on this problem please ?

    A ball rebounds each time to a height which is half that of the previous
    one. If the total distance traveled before coming to rest is 72 meters,
    from how high was the ball dropped?

    thanks a lot
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    The ball falls x m and bounces up 1/2x m and and falls 1/2x m and bounces up 1/4x m....

     \displaystyle x+x+\frac{1}{2}x+\cdots +\frac{1}{2^n}x

    \displaystyle x+x\left(1+\frac{1}{2}+\cdots +\frac{1}{2^n}\right)

    \displaystyle x+x\sum_{n=0}^{\infty}\left(\frac{1}{2}\right)^n=x  +\frac{a}{1-r} Geometric Series.

    \displaystyle a=x, r=\frac{1}{2}

    \displaystyle x+\frac{x}{1-\frac{1}{2}}=72\Rightarrow x+2x=72\Rightarrow 3x=72\Rightarrow x=24
    Last edited by dwsmith; December 18th 2010 at 05:08 PM. Reason: Changed 26 to 24
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  3. #3
    rcs
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    thanks a lot sir. Long Live. God Bless You
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  4. #4
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    Quote Originally Posted by rcs View Post
    Can anybody help me on this problem please ?

    A ball rebounds each time to a height which is half that of the previous
    one. If the total distance traveled before coming to rest is 72 meters,
    from how high was the ball dropped?

    thanks a lot
    Or...

    x+0.5x+0.5x+0.25x+0.25x+0.125x+0.125x+.....=72

    x(2+0.5+0.25+......)=72\ \Rightarrow\ 2x+x(0.5+0.25+....)=72

    x(4+1+0.5+0.25+....)=(2)72\ \Rightarrow\ 5x+x(0.5+0.25+....)=(2)72

    3x=72

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  5. #5
    rcs
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    amazing!
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