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Sum sequence of a geometric series

  1. Jun 22, 2012 #1
    1. The problem statement, all variables and given/known data

    A 'supa-ball' is dropped from a height of 1 metre onto a level table. It always rises to a height equal to 0.9 of the height from which it was dropped. How far does it travel in total until it stops bouncing?


    2. Relevant equations



    3. The attempt at a solution

    The consecutive heights which the ball attains form a geometric series with first term a=1 and common ratio 0.9. Using the formula for the sum to infinity of the series, I am left with S = a/(1-r) = 1/0.1 = 10 metres
    However, the answer given is 19 metres. I don't understand how to get to this answer, is this just a typo?
     
  2. jcsd
  3. Jun 22, 2012 #2
    Hi thekopite! Welcome to PF :smile:

    When the ball moves up 0.9h, it also comes down. You need to include that in your answer :wink:
     
  4. Jun 22, 2012 #3
    Each bounce of the ball has an identical coming down length. For example, if the ball bounces 0.9 metres, it will also come down 0.9 metres, travelling a total distance of 1.8 metres.
     
  5. Jun 22, 2012 #4
    Exactly....Except the first 1m fall :wink:


    Edit : Oops...I thought the OP posted.:uhh:
     
  6. Jun 22, 2012 #5
    thanks, i get it know. feeling a little dumb.
     
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