Question

A tank, travelling at 72 km/hr towards a hill fires a shot and its driver hears the Echo after 4.5 s. Find the distance of the tank from the hill when the shot was fired. (given : velocity of the sound = 350 m/s

Answer 1

Given :

Velocity of tank towards the hill = 72 km/hr

Time after which driver of the tank hears the echo of the shot fired by the tank  = 4.5 sec

Velocity of sound = 350 m/s

To Find :

The distance of the tank from the hill when the tank fired the shot  = ?

Solution :

When the shot was fired , let the distance of the tank from the hill be = 'S'

Time taken by the sound to reach the hill is :

$t = \frac{S}{350} sec$

Since echo is heard after 4.5 sec .

So , the distance travelled by the tank in this time:

=$72 \times\frac{5}{18}\times 4.5 m$

= 90 m

Now the time taken by reflected sound to reach the tank is :

=$\frac{(S-90)}{350} sec$

So , according to the question we have following equation :

∴$\frac{S}{350} + \frac{(S-90)}{350} = 4.5$

Or ,$2S-90 = 350 \times 4.5$

Or ,$2S = 1665$

So , S = 832.5 m

Hence ,the distance of the tank from the hill when the shot was fired is 832.5 m .