Question

A construction worker's helmet slips and falls when he is 500 m above the
ground. He hears the sound of the helmet hitting the ground 11:47 s after
it slipped. Find the speed of sound in air. (g = 10 m/s2).​

Answer 1

T = 11.47 s

g = 10 m/s^2

H = 500m

t after which it will hit can be calculated by

H = 1/2 gt^2

=> t = √ 2h/g

=> t = √ 2 x 500/10 s

=> t = 10 s

So, t after which he will hear the sound is (11.47-10) s = 1.47 s

So, sound will take 1.47 s to travel height of 500 m.

Hence,

v = d/t

=> v = 500/1.47 m/s = 340 m/s (Approx.)

=> v of the sound in air is 340 m/s

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