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 $4.23s$ after it has slipped. Find the speed of sound in air. ( Take $g=9.8m{s}^{-2}$).

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

Answer 1

The correct option is D $341m{s}^{-1}$

Given:
Initial velocity, $u=0m{s}^{-1}$,
Distance the helmet fell, $h=78.4m$
Acceleration due to gravity, $g=9.8m{s}^{-2}$
Total time taken for the sound to be heard, $t=4.23s$

Let $t_1$ be the time taken by the helmet to reach the ground.

From second equation of motion,
$s=ut+\frac{1}{2}\times {at}^2$
$h=\frac{1}{2}g{t}_1^2$
$78.4=\frac{1}{2}\times 9.8\times t_1^2$
$t_1=4s$

The time taken by sound to travel,
$t_2=t-t_1$
$t_2=4.23-4=0.23s$

From definition of speed, the speed of sound in air is:
$v=\frac{s}{t_2}$
$v=\frac{78.4}{0.23}$
$v\approx 341m{s}^{-1}$