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Distance related Series Question (Cal II)

  1. May 17, 2014 #1
    A ball bearing is dropped from a height of 8 meters onto a heavy metal plate. The
    ball bounces each time to a height that is 107 of its preceding height. Assuming that the ball
    continues to bounce indefinitely, find the total distance that it travels.


    I did this:

    Series:

    SUM OF 8(7/10)^k from k=0..infinity. = a/(1-r)= 80/3 m.

    Am I right?
     
  2. jcsd
  3. May 17, 2014 #2

    SammyS

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    Is that a typo?

    Did you mean 7/10 of its previous height?
     
  4. May 17, 2014 #3

    HallsofIvy

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    From what you have below, I presume you mean 7/10 of its preceding height.
    Ok at the first few bounces. It goes down 8 m, then up 8(7/10) then down the same height so it has gone a total of 8+ 8(7/10)+ 8(7/10). It then goes up 8(7/10)(7/10)= 8(7/10)^2 and down 8(7/10)^2. You are missing the "up" portions of the trip.

    Not quite.
     
  5. May 17, 2014 #4
    I meant 7/10
     
  6. May 17, 2014 #5
    Then:

    (SUM OF 8(7/10)^k from k=0..infinity. = a/(1-r)= 80/3 m.)x2-8=45.33 m?
     
  7. May 17, 2014 #6
    Please do tell me if my answer is right.
     
  8. May 17, 2014 #7

    SammyS

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    To the left of the which I inserted is the total downward distance.

    That result to the right looks good for the overall distance.
     
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