Question

A man fired a bullet against a wall and hears an echo after $2s$. He walks $80m$ towards the wall and fired bullet, such that he hears echo after $1s$. Find the distance from wall to the second fired place.

Answer 1

From the given data we have,

$d_{walk}=80m$

$t_1=2s$

$t_2=1s$

$d_2=?$

$v=$ $velocity$ $of$ $sound$

When he fires the bullet, the sound generated travels everywhere, including in the direction towards the wall.

The sound wave travelling towards the wall, hits it, gets reflected from it, moves backwards and reaches his ear.

This is how he hears the echo.

This shows that the sound wave travels twice the distance between him and the wall. Hence, while calculating, we'll have to double the distances.

$2d_1=v\times t_1----------------------\left(1\right)$

$2d_2=v\times t_2----------------------\left(2\right)$

$d_1=d_2+d_{walk}---------------------\left(3\right)$

Dividing equation 2 by 1 we get

$\frac{d_2}{d_1}=\frac{t_2}{t_1}-----------------------\left(4\right)$

Substituting 3 in 4 we get

$\frac{d_2}{d_2+d_{walk}}=\frac{t_2}{t_1}$

$\therefore \frac{d_2}{d_2+80}=\frac{1}{2}$

$\therefore 2d_2=d_2+80$

$\therefore d_2=80m$

The distance from wall to the second fired place is 80 metres.