Velocity Deep
A student drops a stone into a well and hears the sound of the splash 5.0 s later. How deep is the well? The v
A student drops a stone into a well and hears the sound of the splash 5.0 s later. How deep is the well? The velocity of sound is 331 m/s.
S = 1/2 gt^2; where S is the drop distance (well depth) you are looking for; g = 9.81 m/sec^2 on Earth's surface, and t is the time to drop = sqrt(2S/g).
Thus, T = t + S/v = 5 sec the total time since drop; where v is the sound speed = 331 mps. Thus t = T - S/v.
Then sqrt(2S/g) = t = T - S/v; so that 2S/g = T^2 - 2ST/v + (S/v)^2. T, v, and g are given; so you can solve for S...it's a bit messy but doable. Set this up a a quadratic and use the quadratic solution equation to find S.
The key to sovling this is to recognize the two equations for t (the drop time) and then setting them equal.
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