math

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i am having difficulties figuring this out....

a ball has dropped from a height of 15m and bounces 60% of the previous height. the total distance ball travels after the 9th bounce is...

i got this equation done but i do not know how to calculate this to find the answer

15(0.6^9-1)/0.6-1

could you show me how to do it?

  • math -

    the trick here is that the first bounce has a different pattern than the following bounces

    distance of 1st bounce = 15 ,...... just down
    distance of 2nd bounce = 2(15)(.6) , ..... up and down
    distance of 3rd bounce = 2(15)(.6^2)
    distance of 4th bounce = 2(15(.6^3)
    ...
    distance of 9th bounce = 2(15)(.6^8)
    so total distance
    = 15 + 8 terms
    = 15 + 2(15)(.6) [ (.6^8 - 1)/(.6 - 1)]

    I get 59.24

    check my arithmetic

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