Question

A police van moving on a highway with a speed of 30 $\text {km}\;\text h^{-1}$ fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 $\text {km}\;\text h^{-1}$. If the muzzle speed of the bullet is 150 $\text {m}\;\text s^{-1}$, with what speed does the bullet hit the thief’s car ? (Note: Obtain that speed which is relevant for damaging the thief’s car).

Answer 1

Speed of the police van, $\text v_p$ = 30 $\text{km}/\text h$ = 8.33 $\text{m}/\text s$
Muzzle speed of the bullet, $\text v_b$ = 150 $\text{m}/\text s$
Speed of the thief’s car, $\text v_t$= 192 $\text{km}/\text h$ = 53.33 $\text{m}/\text s$
Since the bullet is fired from a moving van, its resultant speed can be obtained as:
= 150 + 8.33 = 158.33 $\text{m}/\text s$
Since both the vehicles are moving in the same direction, the velocity with which the bullet hits the thief’s car can be obtained as:
$\text v_{bt}$= $\text v_b-\text v_t$ = 158.33 – 53.33 = 105 $\text{m}/\text s$