Question

A construction worker’s helmet slips and falls down when he is 78.4 m 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. 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 = 78.4 m and g = 9.8 $m/s^2$
$h=\frac{1}{2}g{t}^2\Rightarrow 78.4=\frac{1}{2}\times \left(9.8\right)\times t^2$
$or{t}^2=\frac{2\times 78.4}{9.8}ort=4sec$
$\therefore$ The time taken by the helmet to drop to the ground = 4 s
The time taken by sound to travel 78.4 m = (4.23 - 4)s = 0.23 s
$\therefore$ The speed of sound in air
$=\frac{78.4m}{0.23s}=340.87m/s\approx 341m/s$