Question

A machine gun is mounted on a tank moving at a speed of $20m{s}^{-1}$ towards a target with the gun pointing in the direction of motion of the tank. The muzzle speed of the bullet equals the speed of sound $=340m{s}^{-1}$. If, at the time of firing, the target is 500 m away from the tank, then

• A. The sound arrives at the target later than the bullet.
• B. The sound arrives at the target earlier than the bullet.
• C. Both sound and bullet arrive at the target at the same time.
• D. The bullet will never arrive at the target.

Answer 1

The correct option is A The sound arrives at the target later than the bullet.

Since only the source of sound, i.e., the gun is in motion, the speed of sound remains unchanged at $340m{s}^{-1}$. Therefore, the time taken by the sound of firing to arrive at the target 500 m away is given by
$t_s=\frac{500}{340}=\frac{25}{17}s$
If the gun points in the direction of motion of the tank, the effective speed of the bullet $=340+20=360m{s}^{-1}$. Therefore, the time taken by the bullet to reach the target is given by
$t_b=\frac{500}{360}=\frac{25}{18}s$
Since $t_s>t_b$, the correct choice is (a).