Question

A police van moving on a highway with a speed of $30km$ $h^{-1}$ fires a bullet at a thief's car speeding away in the same direction with a speed of $192km$ $h^{-1}$. If the muzzle speed of the bullet is $150m{s}^{-1}$ , with what relative speed does the bullet hit the thief's car?

• A. $95m{s}^{-1}$
• B. $105m{s}^{-1}$
• C. $115m{s}^{-1}$
• D. $125m{s}^{-1}$

Answer 1

The correct option is B $105m{s}^{-1}$

$\text{Step 1: Velocity of bullet w.r.t ground}$ $\text{[Refer Fig.]}$

Speeds of Cars:

Police Car: $V_1=30\times \frac{5}{18}m/s=\frac{25}{3}m/s$

Thief's Car: $V_2=190\times \frac{5}{18}m/s=\frac{160}{3}m/s$

$\text{Concept of Muzzle Speed:}$

Muzzle speed is the speed of bullet with respect to the gun, just after firing.

Here the speed of gun is same as that of Police car and bullet is fired in the same direction as the car.

$\therefore V_{muzzle}=V_{b/1}$

$\Rightarrow V_{muzzle}=V_b-V_1,$ Where $V_b$ is the Velocity of bullet w.r.t ground

$\Rightarrow V_b=V_{muzzle}+V_1$

$=150m/s+\frac{25}{3}m/s$

$=\frac{475}{3}m/s$
$\text{Step 2: Velocity of bullet w.r.t. thief's car}$

Velocity of bullet w.r.t thief's car

$V_{b/2}=V_b-V_2$

$=\frac{475}{3}-\frac{160}{3}m/s$
$\therefore V_{b/2}=105m/s$
Hence Option $B$ is correct.