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. ( Acceleration due to gravity $9.8m/s^2$ )

• A. 512 m/s
• B. 215 m/s
• C. 341 m/s
• D. 651 m/s

Answer 1

The correct option is C

341 m/s

Let $t$ be the time taken by the helmet to reach the ground.
Here, $u=0,h=78.4mandg=9.8m/s^2$.
$h=ut+\frac{1}{2}g{t}^2\Rightarrow 78.4=\frac{1}{2}\times \left(9.8\right)\times t^2$
$\Rightarrow t^2=\frac{2\times 78.4}{9.8}\Rightarrow t=4sec$
$\therefore$ The time taken by the helmet to drop to the ground = 4 s.
The time taken by sound to travel $78.4m=(4.23-4)s=0.23s$
$\therefore$ The speed of sound in air$=\frac{78.4m}{0.23s}=340.87m/s\approx 341m/s$