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.

• 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 = 78.4m and g = 9.8 $m/s^2$.
$h=\frac{1}{2}g{t}^2\Rightarrow 78.4=\frac{1}{2}\times \left(9.8\right)\times t^2$
$or{t}^2=\frac{2\times 78.4}{9.8}ort=4s$
$\therefore$ 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 = 0.23 s
$\therefore$ The speed of sound in air
$=\frac{78.4m}{0.23s}=340.87m/s\approx 341m/s$