Question

A boy wants to measure the depth of a well. When he drops a stone from the top of the well, he hears the sound made by the stone hitting the water 1.5 s later. If we can assume that the speed of sound is fast enough to be ignored, how deep is the well?
A. 5.5 m
B. 10 m
C. 11 m
D. 21 m

Answer 1

To solve the problem we apply the motion kinematic equations as well as the techniques used to solve second order polynomial equations.

By definition we know that the height of a body is given by the function

$h = \frac{1}{2}gt^2+v_i*t+h-0$

As there is no initial speed or a distance previously traveled, the equation is:

$h = \frac{1}{2}gt^2$

Where,

g = Gravitational acceleration

t = time

h= Height

Rearranging to find the time we have,

$t = \sqrt{\frac{2h}{g}}$

Then, the sound of the splash take a time $\frac{h}{v}$ to travel back, therefore, in time, it is necessary to adhere the new term, which converts the final time into:

$t = \sqrt{\frac{2h}{g}}\frac{h}{v}$

If we make a similarity to the polynomial equation of the second degree where $x = \sqrt {h}> 0$ we have to:

$\frac{1}{v} x^2 +\sqrt{\frac{2}{g}}x-t = 0$

Solving to find x (which is equivalent to $x ^ 2$) we have to:

$x = \pm 3.253$

Since the positive distance is what allows us to find the actual distance traveled we have finally to

$h = x^2 = 10.58 m$

The correct answer is B.