A police van moving on a highway with a speed of 30 km h^–1 fires a bullet at a thief’s car speeding away in the same direction with a speed of 192 km 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

Speed of the police van, v_p = 30 km/h = 8.33 m/s

Muzzle speed of the bullet, v_b = 150 m/s

Speed of the thief’s car, v_t= 192 km/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 thief’s car can be obtained as:

v_bt = v_b – v_t

= 158.33 – 53.33 = 105 m/s

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