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Pit dropping time difference

  1. Sep 25, 2011 #1
    1. The problem statement, all variables and given/known data
    An object is dropped from rest into a pit and accelerates due to gravity at roughly 10m/s^2. It hits the ground in 5 seconds. A rock is then dropped from rest into a second pit and hits the ground in ten seconds.How much deeper is the second pit. no air resistance.

    2. Relevant equations

    not used

    3. The attempt at a solution
    im pretty sure the answer is 4 times.
    but im not 100%. is it sorta like braking from one velocity to stop then a second(half as much) to stop and finding the distance it takes to stop.because thats four times as long.
     
  2. jcsd
  3. Sep 25, 2011 #2

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    Hey pg! :smile:

    Let's get back to formulas.
    Do you know a relevant formula from which you could calculate the depth of the pit?
     
  4. Sep 25, 2011 #3
    what if i do a=d/t/t
    so it would be 10m/s^2=d/5s/5s
    250m=d

    same formula
    10m/s^2=d/10s/10s
    1000m=d
     
  5. Sep 25, 2011 #4

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    Hmm, "a=d/t/t" is not a correct formula.

    You either should have [itex]a = {d^2x \over dt^2}[/itex],
    or what would suit your problem:
    [tex]d = {1 \over 2}g t^2[/tex]
     
  6. Sep 25, 2011 #5
    but a=d/t/t is eaual to a=v/t
     
  7. Sep 25, 2011 #6

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    Not quite.
    v=d/t gives you the "average" speed during the entire drop.
    The actual speed starts at zero and increases to some maximum.
    Assuming the acceleration is constant, the corresponding acceleration is actually a=2 d/t/t.

    In other words, you cannot just use "a=v/t" or "v=d/t".
    You should use: "d=d0 + v0 t + (1/2)a t^2" (assuming acceleration a is constant).
    And: "v=v0 + a t" (again assuming a is constant).
     
  8. Sep 25, 2011 #7
    okay well i used this and still got four.
     
  9. Sep 25, 2011 #8

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    Yep! :smile:

    (Sorry to drag this out, but now you did it with the proper formula. :wink:)
     
  10. Sep 25, 2011 #9
    haha its okay as long as i understand.i wanna do well on my test.:)
     
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