Question

helmet of a construction worker fall from height 78.4 metre above the ground he hear the sound of the helmet hitting the ground 4.23 seconds after it Falls find the speed of sound in air.

Answer 1

distance covered by the sound = 78.4m
time taken to reach the top of the building = 4.23 sec
now d= v*t
78.4= 4.23*v
therefore 78.4/4.23 = v
18.534 m/s

Answer 2

Answer :

Let t be the time taken by the helmet to reach the ground.

We have,

$\text{h = ut }+ \frac{1}{2} \: \text{ gt} {}^{2}$
Here,

u = 0, h = 78.4 m, g = 9.8 m/s²

$78.4 = \frac{1}{2} \times (9.8) \times \text t {}^{2} \\ \\ \text t {}^{2} = \frac{2 \times 78.4}{9.8} \\ \\ \text t {}^{2} = \frac{1568}{9.8} \\ \\ \text t = 4 \text { seconds}$
∴ the time taken by the helmet to reach the ground = 4 secs.

The time taken by sound to travel 78.4 m = ( 4.23 - 4 ) s

⇒ 0.23 secs.

∴ the speed of sound in air = 78. 4 / 0.23 m/s

= 341 m/s.