Question

A construction worker's helmet slips and falls when he is 78.4m above the ground. He hears the sound of the helmet hitting the ground 4.23 seconds after it slipped. Find the speed of the sound on air.

Answer 1

To get the time taken by the helmet to reach the ground

s = ut + 1/2 at²  We take a = 10 m/s² = Acceleration due to gravity
     And initial velocity u = 0

∴ s = 1/2 at²
78.4 = 1/2 x 10 x t²
t² = 15.68
t = 3.96 sec.
Time taken for sound to travel = 4.23 - 3.96 =  0.27 sec.
Speed of sound = Dist/Time = 78.4/0.27 = 290.37 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.