Aboy 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

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

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

Where,

g = Gravitational acceleration

t = time

h= Height

Rearranging to find the time we have,

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

If we make a similarity to the polynomial equation of the second degree where we have to:

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

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

The correct answer is B.