Question

A road runs between two parallel rows of buildings. A motorist moving just in the middle with a velocity of $30km/h$, sounds the horn. He hears an echo one second after sounding the horn. Find the distance (in metre) between the two rows of the buildings. The velocity of sound $=330m/s$

Answer 1

Answer: 329.9

Suppose $2y$ is the distance between two rows of the buildings. The distance travelled by car in 1 second

$x=\left(30\times \frac{5}{18}\right)\times 1=8.33m$
The distance travelled by sound in 1 second
$2\ell =330\times 1=330m$
$\therefore \ell =165m$
From the figure $y=\sqrt{{\ell }^2-{\left(\frac{x}{2}\right)}^2}$
$=\sqrt{165^2-{\left(\frac{8.33}{2}\right)}^2}$
$=164.95m$
Thus the distance between two rows of the buildings $2y=329.9m$