Explanation

(c) Let the man $M$ be at a distance $x$ from hill $H_{1}$ and $y$ from hill $H_{2}$ as shown in figure. Let $y > x.$
[image:15_image90.png]
The time interval between the original sound and echoes from $H_{1}$ and $H_{2}$ will be respectively
$t_{1} = \frac{2x}{v}$ and $t_{2} = \frac{2y}{v}$
where $v$ is the velocity of sound
The distance between the hills is
$x + y = \frac{v}{2}\left( t_{1} + t_{2} \right) = \frac{340}{2}\lbrack 1 + 2\rbrack = 510\ m$