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 speed does the bullet hit the thief’s car? (Note: Obtain that speed which is relevant for damaging the thief’s car).

Answer 1

Find the relative velocity of bullet with respect to police van.

Given, speed of the police-van,

$v_p=30km/h=8.33m/s$

Muzzle speed of the bullet,

$v_m=150m/s$

Speed of the thief's

$v_t=192km/h=53.33m/s$

Since, the bullet is fired from a moving van, the speed of moving van needs to be added to muzzle speed of bullet. Therefore, speed of bullet is:-

$v_{bp}=150m/s$

$v_b=150+v_p$
$=150+8.33$
$=158.33m/s$.
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:
$v_b=v_b-v_t$
= 158.33- 53.33
=105 m/s