Question

A construction worker's helmet slips and falls when he is $78.4\text{m}$ above the ground. He hears the sound of the helmet hitting the ground $4.23$ seconds after it slipped. Find the speed of sound (in SI units) in air.

• A. $343$
• B. $344$
• C. $341$
• D. $342$

Answer 1

The correct option is C $341$

Let t be the time taken by the helmet to reach the ground.
We have,
$h=ut+\frac{1}{2}g{t}^2$
Here
$u=0,h=78.4\text{m},g=9.8\text{m}/s^2$

$\therefore$ $78.4=\frac{1}{2}\times \left(9.8\right)\times t^2$
or $t^2=\frac{2\times 78.4\text{m}}{9.8\text{m}/s^2}$
$t=4$ seconds.
$\therefore$ The time taken by the helmet to drop to the ground $=4\text{s}$.
The time taken by sound to travel $78.4\text{m is}(4.23-4)\text{s}=0.23\text{s}.$
$\therefore$ The speed of sound in air $=\frac{78.4\text{m}}{0.23\text{s}}=340.87\text{m/s}\approx 341\text{m/s}$