Science Question on Propagation of Sound

Question

A stone is dropped from the top of a tower 500 m high into a pond of water at the base of the tower. When is the splash heard at the top?
Given, g = 10 ms–2 and speed of sound = 340 ms–1.

Accepted Answer

Tower Height (s): 500 m
Sound Velocity (v): 340 m/s
Gravity Acceleration (g): 10 m/s²
Stone's Initial Velocity (u): 0

Time (t 1) taken by the stone to fall to the tower base:
Applying the second equation of motion,
$s=ut_1+\frac{1}{2}g(t_1)^2$

500=0⋅ t 1+ $\frac{1}{2}$ ⋅10⋅(t 1)2
(t 1)2=100
t 1=10s

Time (t 2) taken by sound to reach the top from the tower base:
t 2 = $\frac{s}{v}$ = $\frac{500}{340}$ $≈$ 1.47s

Total time (t) is the sum of t 1 and t 2:
t 1+t 2=10+1.47=11.47s