Question

A police van moving on a highways with a speed of 30km/hr fires a bullet at a thief’s car speeding away in the same direction with a speed of 192km/h If the speed of the bullet with respect to police van is 150 m/s with that what relatives speed does the bullet hit the thief's car?”

Answer 1

Hint
As we have to find the relative's speed, does the bullet hit their car so we can say that we have to find the velocity of the bullet with respect to the thief.
As from the given situation we can assume that the velocity of the bullet fired by the police is equal to the final velocity of the bullet muzzle from the gun.

Complete step-by-step answer:
As we have given that
Velocity of the police $v_p = 30km/h$
Or $v_p$ = $\dfrac{{25}}{3}$m/s
And velocity of the thief = 192km/h
Or $v_t$ = $\dfrac{{160}}{3}$m/s
Velocity of bullet with respect to police van $v_{bp} = 150 m/s$
$v_{bp} = v_b - v_p$
SO velocity if bullet is $v_b = v_{bp} + v_p$
$\Rightarrow v_b = 150 + \dfrac{25}{3} m/s$
$\Rightarrow v_b = \dfrac{{475}}{3}$m/s
So assuming the velocity of the thief is zero and seen with respect to the thief then
$\Rightarrow v_bt = v_b - v_t$
$\Rightarrow v_bt = \dfrac {475}{3} - \dfrac{160}{3}$
$\Rightarrow v_bt = \dfrac{315}{3}$
$\Rightarrow v_bt =105 m/s$
Velocity of bullet with respect to the thief's car is $105 m/s$.

Note
Relative velocity can be defined as the velocity of an object or observer B in the rest frame of another object of observer A. Its example be like motion of aero plane in the wind or moving boats through the water.