Question

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

Answer 1

HELLO DEAR,



H =78.4 meter

g=9.81m/s²



u=initial spped=0

TIME TAKEN TO HEAR THE SOUND = τ = 4.23 sec

a) Speed of helmet (v = ?)

Use kinematics engine (free fall)

v 2 = u 2 + 2gh

= 0 + 2gh

$v = \sqrt{2 \times g \times h } \\ = > \sqrt{2 \times9.81 \times 78.4 } \\ = > 39.22 \frac{m}{s}$

Time taken by helmet to reach the ground is t = ?

Use kinematics egh.

v = u + gt

$39.22 = 0 + 9.81 \times t \\ = > t = \frac{39.22}{9.81} \\ = > t = 3.99s$
τ-t =4.23-3.99 =0.24s



In this time sound travels the height 78.4 m

So, speed of sound in air = 

$= > \frac{78.4}{0.24} = 326.67 \frac{m}{s}$

I HOPE ITS HELP YOU DEAR
, THANKS

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.