Finding height of a well using speed of sound

  1. 1. The problem statement, all variables and given/known data
    The problem is you drop a coin into a well then 3 second later you hear the splash. With this information find out the height of the well.

    Assume 343 m/s is the speed of sound and neglect any effects due to air resistance.

    g = acceleration due to gravity = 9.8 m/s^2
    v0 = initial velocity = 0 m/s
    v1 = final velocity
    H = height
    t1 = initial time = 0 s
    t2 = time at final velocity

    2. Relevant equations
    H = (v0^2 - v1^2)/2g

    v1 = v0 - g(t2 - t1)


    3. The attempt at a solution
    Reduced equation to H = v0^2/2g and found v0 to be -9.8m/s^2(3s - 343m/s(t2))

    I'm mainly having trouble trying to find out how much time was taken off for the sound of the splash reaching you.

    Any help is appreciated.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Doc Al

    Staff: Mentor

    Instead of trying to relate distance to speed, which you have no information about, relate distance to time. Use a different kinematic relationship.

    Think of the total time as having two parts:
    (1) The time it takes for the coin to reach the water
    (2) The time it takes for the sound to go from the water to the top of the well

    For the second time, realize that sound travels at a constant speed.
     
  4. The coin falls down to the bottom of the well in time [tex]t_1[/tex]. The sound travels up, at velocity s, to your ear in time [tex]t_2[/tex]. Now we can write 3 basic equations.

    << equations deleted by berkeman >>

    We have three unknowns and threee equations, that means that we can solve and figure out h.
     
    Last edited by a moderator: Sep 2, 2009
  5. berkeman

    Staff: Mentor

    Please let the OP figure out those equations on their own. They must do the bulk of the work on their homework/coursework problems.
     
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