Question

A person is in front of a vertical mountain fires a bullet and hears its echo after a time 3 s. The person walks a distance 'd' towards mountain then fires another bullet and hears its echo after a time 2 s. If velocity of sound in air is 340 ms${}^{-1}$, the value of 'd' is

• A. 85 cm
• B. 170 m
• C. 255 m
• D. 340 m

Answer 1

The correct option is B 170 m

Given,

Velocity of sound $v=340$

Case-1: Echo is heard in 3 sec, let the distance between the mountain and the person is $x$.

Total distance travel by sound $=2x=vt$

Distance from mountain in first case $x=\frac{vt}{2}$ $=\frac{340\times 3}{2}$

Case-2: Echo is heard in 2 sec, let the distance between the mountain and the person is $y$.

Total distance travel by sound $=2y=v{t}^{\prime }$

Distance from mountain in second case $y=\frac{340\times 2}{2}$

Walking distance $d=x-y$

$\therefore d=\frac{340\times 3}{2}-\frac{340\times 2}{2}=\frac{340}{2}=170m$

Option B