Question

A construction worker’s helmet slips and falls down when he is $78.4m$ above the ground. He hears the sound of the helmet hitting the ground $4.23$ seconds after it has slipped. Then find the speed of the sound in air.

• A. $512m{s}^{-1}$
• B. $215m{s}^{-1}$
• C. $341m{s}^{-1}$
• D. $651m{s}^{-1}$

Answer 1

The correct option is C

$341m{s}^{-1}$

Let $t$ be the time taken by the helmet to reach the ground.
Here, initial velocity, $u=0m{s}^{-1}$
Height, $h=78.4m$
Acceleration due to gravity, $g=9.8m{s}^{-2}$.
Using the third equation of motion, $h=ut+\frac{1}{2}g{t}^2$
$\Rightarrow$$h=\frac{1}{2}g{t}^2$
$\Rightarrow 78.4=\frac{1}{2}\times \left(9.8\right)\times t^2$
$or{t}^2=\frac{2\times 78.4}{9.8}ort=4sec$
$\therefore$ The time taken by the helmet to drop to the ground = $4s$
The time taken by sound to travel $78.4m=4.23-4=0.23s$
$\therefore$ The speed of sound in air
$=\frac{Distancetravelled}{Timetaken}=\frac{78.4}{0.23}=340.87m{s}^{-1}\approx 341m{s}^{-1}$