Question

A road runs mid-way between two parallel rows of building. A motorist moving with a velocity of $36 \,km \,h ^{-1}$ sounds the horn. He hears the echo 1 sound after he has sounded the horn. If velocity of sound is $330 \,m \,s ^{-1},$ then the distance between the two rows of building is

• A. $2 \sqrt{165^{2}-5^{2}} m$
• B. $\sqrt{165^{2}-5^{2}} m$
• C. $\sqrt{330^{2}-10^{2}} m$
• D. $2 \sqrt{330^{2}-10^{2}} m$

Answer 1

Answer: (A)

$v_{\text {car }}=\frac{36 km }{ h }=10 m / s$
Let the car travel from $C_{1}$ to $C_{2}$ in 1 sec.
so $C_{1} C_{2}=(10 m / s )(1 s )=10 m$
Hence $C_{1} M=(10 / 2) m =5 m$
Sound travels from $C_{1}$ to $R$ and $R$ to $C_{2}$ in $1 s$,
then $C_{1} R=(330 m / s )(0.5 s )$
$=165 m$
Using Pythagoras theorem,

$\left(\frac{A}{2}\right)^{2}=165^{2}-5^{2}$
$d=2 \cdot \sqrt{165^{2}-5^{2}} m$