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 = (1)/(2)gt^2+v_i*t+h-0`

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

`h = (1)/(2)gt^2`

Where,

g = Gravitational acceleration

t = time

h= Height

Rearranging to find the time we have,

`t = \sqrt{(2h)/(g)}`

Then, the sound of the splash take a time
`(h)/(v)` to travel back, therefore, in time, it is necessary to adhere the new term, which converts the final time into:

`t = \sqrt{(2h)/(g)}(h)/(v)`

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

`(1)/(v) x^2 +\sqrt{(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.