Question

A road runs midway between two parallel rows of buildings. A motorist moving with a speed of $36km{h}^{-1}$ sounds the horn. He hears the first echo one second after he has sounded the horn. Speed of sound in air is $330m{s}^{-1}$ . Then The distance between the two buildings and the time after which he hears second echo are

• A. 350 m, 2.5 s
• B. 329.8 m, 2s
• C. 360 m, 2.3 s
• D. 300.2m, 1.5 s

Answer 1

The correct option is B 329.8 m, 2s

Motorist is travelling with a velocity $v=36\times \frac{5}{18}=10m{s}^{-1}$

So.
MD = 10 m
He hears first echo after 1 s. So, when he travels a distance MD he hears first escho (i.e. at D).
In this time, distance travelled by sound = MA + AD = 330m
$\therefore$ AD=165 m
$\therefore y^2+5^2={165}^2\Rightarrow$ y=164.9 m
So, required distance = 2y = 329.8 m
He hears the second echo, when he is at point E. So, the time after which he hears second echo is 2 seconds from the instant of sounding the horn.