Question

A person standing at a distance $x$ in front of a cliff fires a gun. Another person B standing behind the person A at a distance $y$ from the cliff hears two sounds of the fired shots after $2s$ and $3s$ respectively. Calculate $x$ and $y$ (take speed of sound 320 $m{s}^{-1}$)​

Answer 1

Given:
Distance of A from cliff $=x$
Distance of B from cliff $=y$
B hears the first shot after 2 s,
and the second shot after 3 s
Speed of sound $=320m/s$
We know,
$\text{Speed}=\frac{Distance}{Time}$

The person B hears two versions of the fired shot, one directly from the gun and another after reflection from the cliff.
When sound reached B directly:
Distance travelled by the sound = y - x
.'. $320=\frac{y-x}{2}\Rightarrow y-x=640$ ----(1)
When sound reached B after reflection:
Distance travelled by the sound = y + x
.'. $320=\frac{y+x}{3}\Rightarrow y+x=960$ ----(2)
From equation (1) and (2),
y - x = 640
y + x = 960
Upon solving, we get
y = 800 m, x = 160m