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Using integration to find depth

  1. Nov 5, 2012 #1
    1. The problem statement, all variables and given/known data
    Your mobile phone drops down a sinkhole. You hear it hit the bottom 8.5 seconds later. How deep is the hole?
    Assume there is no air resistance
    velocity of sound 334m/s
    gravity 9.8m/s
    2. Relevant equations



    3. The attempt at a solution
    I tried integrating the equation using just the acceleration; however, I believe that the velocity of sound needs to be incorporated aswell. So I started with a(t)=9.8 then integrated to get 9.8t +c, then I made t=0 v=0 and so c=0 and integrated again to get 4.9t^2 +c, I'm not sure where to go from here.
     
    Last edited: Nov 5, 2012
  2. jcsd
  3. Nov 5, 2012 #2

    tiny-tim

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    hi jackscholar! :smile:

    do it the other way round …

    find the time it takes to fall a distance x, then add the time for the sound to return from that distance,

    then put that equal to 8.5, and solve for x :wink:
     
  4. Nov 5, 2012 #3
    all I can think of is 8.5=9.8x + ?? for some reason I keep going back to 8.5=9.8x+x/334
     
  5. Nov 5, 2012 #4

    tiny-tim

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    what is the time taken to fall a distance x (from rest)?
     
  6. Nov 5, 2012 #5
    I'm sorry but i have absolutely no idea
     
  7. Nov 5, 2012 #6
    I shall sleep on it. Thank you for all your help, as always you've given me something to think about.
     
  8. Nov 5, 2012 #7
    Hint:

    Determine the time for the sound to go from bottom of pit to top. If depth is y then

    dt = y/334 seconds

    Use free fall equation to determine depth of hole.

    y = 0.5 * a * t^2 where

    t = total time minus the time for the sound to get from bottom to top
    a = 9.8 m/sec^2
     
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