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Free fall problems

  1. Jan 27, 2010 #1
    1. The problem statement, all variables and given/known data

    You drop a stone into a deep well and hear it hit the bottom 4.00 s later. This is the time it takes for the stone to fall to the bottom of the well, plus the time it takes for the sound of the stone hitting the bottom to reach you. Sound travels about 343 m/s in air. How deep is the well?

    2. Relevant equations

    distance travelled by stone = distance travelled by sound

    v0 t + 1/2 at square = v0t + 1/2 at square

    3. The attempt at a solution

    0 +1/2 * 9.8 * t square = 343 ( 4-t) +0
  2. jcsd
  3. Jan 27, 2010 #2


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    So far so good. Can you solve this equation for t?
  4. Jan 27, 2010 #3
    I am not sure you are on the right track with what you are doing. First, you know that the well is x meters deep. and that it takes x/343 seconds for the sound to travel to the top. so that means that the stone takes (4-x/343) seconds to fall. You know that initial velocity is 0 so you are left with the following equation.

    x = ((-9.8) * (4 - x/343)²)/2

    it will be a quadratic that you have to solve.

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