Question

A policeman moving on a highway with a speed of $30{\text{kmh}}^{-1}$ fires a bullet at a thief's car speeding away in the same direction with a speed of $192{\text{kmh}}^{-1}$. If the muzzle speed of the bullet is $150{\text{ms}}^{-1}$ with what speed does the bullet hit the thief's car?

• A. $120\text{m/s}$
• B. $90\text{m/s}$
• C. $125\text{m/s}$
• D. $105\text{m/s}$

Answer 1

The correct option is D $105\text{m/s}$

Given:

Velocity of police van w.r.t. ground is
$v_{pg}=30\times \frac{5}{18}=\frac{25}{3}\text{m/s}$

Muzzle speed of the bullet is
$v_b=150{\text{ms}}^{-1}$

So, speed of the bullet w.r.t ground will be

$v_{bg}=(150+25/3){\text{ms}}^{-1}$

Velocity of thief's car w.r.t. ground is
$v_{tg}=192\times \frac{5}{18}=\frac{160}{3}\text{m/s}$

$\therefore$ relative velocity of the bullet w.r.t. the thief's car is given by

$v_{bt}=v_{bg}-v_{tg}=150+\frac{25}{3}-\frac{160}{3}=150-\frac{135}{3}$

$\therefore v_{bt}=105\text{m/s}$

Hence, $\left(d\right)$ is the correct answer.

$$\begin{array}{c}\text{Why this question?}\\ \text{Velocity of bullet with respect to ground}\\ \text{= Velocity of bullet with respect to gun}\\ \text{+ velocity of gun with respect to ground}\end{array}$$