Question

A police jeep travelling at a speed of $45\text{km/h}$ is chasing a thief's car moving at a speed of $153\text{km/h}$. If police fire a bullet with a muzzle velocity of $180\text{m/s}$, the velocity with which it strikes the thief's car is

• A. $54\text{m/s}$
• B. $150\text{m/s}$
• C. $450\text{m/s}$
• D. $250\text{m/s}$

Answer 1

The correct option is B $150\text{m/s}$

Effective speed of the bullet, $V_b=$ muzzle velocity $+$ speed of police jeep
$\Rightarrow V_b=180\text{m/s}+45\text{km/h}$
$\Rightarrow V_b=180\text{m/s}+12.5\text{m/s}$
$\Rightarrow V_b=192.5\text{m/s}$
Speed of thief, $V_t=153\text{km/h}=42.5\text{m/s}$
Velocity of bullet w.r.t. thief's car,
$V_{b,t}=V_b-V_t$
$V_{b,t}=192.5-42.5=150\text{m/s}$