A police van moving on a highway with a speed of $30 k m / h r$ fires a bullet at a thief's car speeding away in the same direction with a speed of $192 k m / h r$ . If the muzzle speed of the bullet is $150 m / s$ , 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

Speed of the police van, $v_{p} = 30 k m / h = 8.33 m / s$
Muzzle speed of the bullet, $v_{b} = 150 m / s$
Speed of the thiefs car, $v_{t} = 192 k m / h = 53.33 m / s$
Since the bullet is fired from a moving van, its resultant speed can be obtained as:
$= 150 + 8.33 = 158.33 m / s$
Since both the vehicles are moving in the same direction, the velocity with which the bullet hits the thiefs car can be obtained as:
$v_{b t} = v_{b} - v_{t}$
$= 158.33 - 53.33 = 105 m / s$

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