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. Find the speed of sound in air.$(takeg=9.8m/s^2)$.

• 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 of helmet, u = 0
Height of building h = $78.4m$ and g = $9.8m/s^2$.
$h=\frac{1}{2}g{t}^2$
$78.4=\frac{1}{2}\times \left(9.8\right)\times t^2$
or, $t^2=\frac{2\times 78.4}{9.8}$
or, $t=4s$
$\therefore$ The time taken by the helmet to drop to the ground = $4s$.
The time taken by sound to travel $78.4m$ = $(4.23-4)s$ = $0.23s$
$\therefore$ The speed of sound in air $=\frac{78.4m}{0.23s}=340.87m{s}^{-1}\approx 341m{s}^{-1}$