Question

A person drops a stone down a well and hears the echo 8.9 s later. if it takes 0.9 s for the echo to travel up the well, approximately how deep is the well?

Answer 1

Total time in between the dropping of the stone and hearing of the echo = 8.9 s

Time taken by the sound to reach the person = 0.9 s

Time taken by the stone to reach the bottom of the well = 8.9 - 0.9 = 8 seconds

Initial speed (u) = 0 m/s

Acceleration due to gravity (g) = 9.8 m/s^2

Time taken (t) = 8 seconds

Let the depth of the well be h.

Using the second equation of motion:

$h = ut + \frac{1}{2}\times a \times t^2$

$h = 0 \times 8 + \frac{1}{2} \times 9.8 \times 8^2$

h = 313.6 m

Hence, the depth of the well is 313.6 m