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:
[tex]h = ut + \frac{1}{2}\times a \times t^2[/tex]
[tex]h = 0 \times 8 + \frac{1}{2} \times 9.8 \times 8^2[/tex]
h = 313.6 m
Hence, the depth of the well is 313.6 m
