Question

A person standing between two parallel hills fires a gun. He hears the first echo after 1.5 s and second after 2.5 s. If speed of sound is 332m/s, then the distance between the hills is

Answer 1

Given:

A person standing between two parallel hills fires a gun. He hears the first echo after 1.5 s and second after 2.5 s.

To find:

Distance between the hills.

Calculation:

Let distance from man to 1st hill be x and distance from man to 2nd hill be y ;

In 1st case:

• Sound wave travels from the gun towards the first hill, gets reflected back and reaches the man after 1.5 seconds.

$\therefore \: 2x = 332 \times 1.5$

$= > \: x = 166 \times 1.5$

$= > \: x =249 \: m$

In 2nd case:

• Sound travels from the gun towards the second hill, gets reflected back and reaches the man after 2.5 seconds.

$\therefore \: 2y = 332 \times 2.5$

$= > \: y = 166\times 2.5$

$= > \: y = 415 \: m$

So, distance between the two hills :

$\therefore \: d = x + y$

$= > \: d = 249 + 415$

$= > \: d = 664 \: m$

So, final answer is:

$\boxed{ \bold{\: d = 664 \: m}}$