A stone dropped from the top of a tower of height 300 m high splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is 340 m s-1? (g= 9.8 m s-2)
Height of the tower, s = 300 m
Initial velocity of the stone, u = 0
Acceleration, a = g = 9.8 m/s2
Speed of sound in air = 340 m/s
The time (t1) taken by the stone to strike the water in the pond can be calculated using the second equation of motion, as:
s = ut1 + 1/2 gt21
300 = 0 + 1/2 x 9.8 x t12
∴ t1 = underroot [(300 x 2) / 9.8]
= 7.82 s
Time taken by the sound to reach the top of the tower, t2 = 300/340 = 0.88 s
Therefore, the time after which the splash is heard, t = t1 + t2
= 7.82 + 0.88 = 8.7 s
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