(796) Problem 12: Suppose a person drops a pebble into a dark well and, using pr

Question

(796) Problem 12: Suppose a person drops a pebble into a dark well and, using pr elapses until the sound of the splash reaches your ear equipment, you measure the time that 50% Part (a) Neglecting the time required for sound to travel up the well, calculate the depth to the surface of the water, in meters, if the sound returns in 2.1 s. 50% Part (b) Now calculate the well's depth to the surface ofthe water in meters, taking into account the time for sound to travel up the well. The speed of sound is 330.5 m/s in this well. Grade Summary Deductions 0% Potential 100%

Explanation / Answer

Let h be the depth of the well, g is the acceleration of gravity (9.8 m/s) and v is the speed of sound (340 m/s)

After the rock is released, the time it takes to reach the water is: sqrt (2h / g)

Then, the sound of the splash take a time h/v to travel back

t = sqrt (2h / g) + h/v

This is a quadratic equation for the unknown x = sqrt(h) > 0

(1/v) x^2 + sqrt(2/g) x - t = 0

(1/330.5) x^2 + sqrt(2/9.8) x - 2.1 = 0

We discard the negative solution of that equation and retain the positive one:

x = 4.51

h = x^2 = 20.34 m

Please rate my answer, good luck...

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