# How to determine the depth of a water well given the initial velocity, the time and the speed of sound?

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How to determine the depth of a water well, knowing that the time between the initial instant in which a stone is released with zero initial velocity and that in which noise is heard, as a consequence of the impact of the stone on the bottom, is #t = 4.80\ s# . Ignore the air resistance and take the sound speed of #340 m / s# .

How to determine the depth of a water well, knowing that the time between the initial instant in which a stone is released with zero initial velocity and that in which noise is heard, as a consequence of the impact of the stone on the bottom, is

##### 1 Answer

(I have used the approximation

#### Explanation:

Let

So, the depth of the well is given by

Putting in the values, we get the following equation for

This can be solved to yield

Keeping the positive root yields

This gives