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Finding cliff height

  1. Jan 24, 2013 #1
    1. The problem statement, all variables and given/known data

    Suppose you are climbing in the high sierra when you suddenly find yourself at the edge of a fog shrouded cliff. To find the height of this cliff, you drop a rock from the top and 10 s later, hear the sound of it hitting the ground at the foot of the cliff.
    a) Ignoring air resistance, how high is the cliff if the speed of sound is 330 m/s?
    b) Suppose you had ignored the time it takes the sound to reach you. In that case, would you have overestimated or underestimated the height of the cliff? Explan your reasoning.

    2. Relevant equations

    y=yo+vo*t+1/2*a*t^(2)

    -b +or- [Sqrt(b^(2)-4ac)]/2a

    3. The attempt at a solution
    t1=time for the rock to fall to the ground.
    t2=time for the sounds to go from bottom to top of cliff

    t1+t2=10seconds

    For rock falling down:

    y=yo+vo*t+1/2*a*t^(2)

    0=H-4.905m/s^(2)*t1^(2)

    For sound coming up from the bottom:

    y=yo+vo*t+1/2*a*t^(2)

    H=330m/s*t2 - 4.905m/s^(2)*t2^(2)

    substitute t2 with (10seconds-t1) and then equate the equations from sound and rock.

    4.90m/s^(2)*t1^(2)=330m/s(10s-t1)-4.905m/s^(2)(10s-t1)^(2)

    I end up with 9.81m/s^(2)*t1^(2) + 231.9m/s*t1-2809.5m

    I use the quadratic formula to get this

    t1=8.8224 seconds

    I end up with H=381.7850m.

    I do not get part b though.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Jan 24, 2013
  2. jcsd
  3. Jan 24, 2013 #2

    tms

    User Avatar

    Be careful with how you write the equations. Neither of these is correct.
    This is also not correct.
    When working problems, it is always best to solve the problem symbolically, and only plug in numbers at the very end. One problem with plugging in numbers in the beginning is that you force your readers to figure out what the numbers are and where they come from.
    Why the second term on the right?
    What don't you get about it?
     
  4. Jan 25, 2013 #3

    rude man

    User Avatar
    Homework Helper
    Gold Member

    Sound is not subject to gravity!
     
  5. Jan 25, 2013 #4
    So for sound 1/2*a*t^(2) should go to zero right? Got it thanks guys!
     
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