Question

A road runs between two parallel rows of buildings. A motorist moving just in the middle with a velocity of $30\, km/h$, 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 $= 330\, m/s$

Answer 1

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

$x=\left(30\times\frac{5}{18}\right)\times1 = 8.33\,m$
The distance travelled by sound in 1 second
$2\ell = 330\times1=330\,m $
$\therefore \ell=165\,m $
From the figure $y=\sqrt{\ell^{2}-\left(\frac{x}{2}\right)^{2}}$
$=\sqrt{165^{2}-\left(\frac{8.33}{2}\right)^{2}}$
$=164.95\,m $
Thus the distance between two rows of the buildings $2y= 329.9 m$