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

speed of sound 320 ms^-1

As we know,

Speed = ${\displaystyle \frac{\text{distance}}{\text{time}}}$

The person B hears two sounds of the fired shot, the first one is direct from the gun while another sound comes after reflection from the cliff

In the case of first sound for person B, when t = 2s (i.e., when the gun was fired)

Substituting the values in the formula above, we get,

${\displaystyle 320=\frac{y-x}{2}}$

y - x = 640

Hence, y - x = 640 m    ...(i)

In the case of second sound for person B, when t = 3s (i.e. after reflection from the cliff)

Substituting the values in the formula above, we get,

${\displaystyle 320=\frac{y+x}{3}}$

y + x = 960

Hence, y + x = 960 m     ...(ii)

Adding equation (i) and (ii), we get,

y - x = 640
y + x = 960 
2y = 1600

y = ${\displaystyle \frac{1600}{2}}$

⇒ y = 800 m

Therefore, y = 800 m

Substituting the value of y in eqn (i) we get the value of x,

800 - x = 640

⇒ x = 800 - 640

⇒ x = 160

Therefore, x = 160 m

Hence, x = 160 m and y = 800 m