You stand at the top of a deep well. To determine the depth, D, of the well you

Question

You stand at the top of a deep well. To determine the depth, D, of the well you drop a rock from the top of the well and listen to the splash as the rock hits the waters surface. The sound of the splash arrives t= 3.6 s after you drop the rock. The speed of sound in the well is v = 339 m/s.
A). Solve the quadratic equation for the depth of the well, D, and calculate its value in meters. You stand at the top of a deep well. To determine the depth, D, of the well you drop a rock from the top of the well and listen to the splash as the rock hits the waters surface. The sound of the splash arrives t= 3.6 s after you drop the rock. The speed of sound in the well is v = 339 m/s.
A). Solve the quadratic equation for the depth of the well, D, and calculate its value in meters.
A). Solve the quadratic equation for the depth of the well, D, and calculate its value in meters.

Explanation / Answer

T = T1 + T2 = 3.6 sec

T1 = time taken by rock to reach bottom

T2 = time taken by sound of splash to reach on surface

D = 0.5*g*T1^2

D = Vs*T2

0.5*g*T1^2 = Vs*T2

0.5*9.81*T1^2 = 339*(3.6 - T1)

4.905*T1^2 + 339*T1 - 339*3.6 = 0

Solving above quadratic equation

T1 = 3.43 sec

Now

D = 0.5*9.81*T1^2

D = 0.5*9.81*3.43^2 = 57.71 m

Or

T2 = 3.6 - 3.43 = 0.17 sec

D = 339*0.17 = 57.63 m

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