Question

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

$v_{\text{car }}=\frac{36km}{h}=10m/s$
Let the car travel from $C_1$ to $C_2$ in 1 sec.
so $C_1{C}_2=(10m/s)(1s)=10m$
Hence $C_{1}M=(10/2)m=5m$
Sound travels from $C_1$ to $R$ and $R$ to $C_2$ in $1s$,
then $C_{1}R=(330m/s)(0.5s)$
$=165m$
Using Pythagoras theorem,

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