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 m s−2 and speed of sound = 340 m s−1.

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 m s−2 and speed of sound = 340 m s−1.

Accepted Answer

Solution:
Height (s) of tower = 500 m
Velocity (v) of sound = 340 m s&minus;1
Acceleration (g) due to gravity = 10 m s&minus;1
Initial velocity (u) of the stone = 0
Time (t1) taken by the stone to fall to the tower base:
As per the second equation of motion,
s= ut1 + (&frac12;) g (t1)2
500 = 0 x t1 + (&frac12;) 10 (t1)2
(t1)2 = 100
t1 = 10 s
Time (t2) taken by sound to reach the top from the tower base = 500/340 = 1.47 s
t = t1 + t2
t = 10 + 1.47
t = 11.47 s

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