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

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Solution

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

Given, speed of the police-van,

$v_{p} = 30 k m / h = 8.33 m / s$

Muzzle speed of the bullet,

$v_{m} = 150 m / s$

Speed of the thief's

$v_{t} = 192 k m / h = 53.33 m / s$

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:-

$v_{b p} = 150 m / s$

$v_{b} = 150 + v_{p}$
$= 150 + 8.33$
$= 158.33 m / s$ .
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

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