A Police Van Moving On A Highway With A Speed Of 36 Km H–1 fires A Bullet At A Thief’s Car Speeding Away In The Same Direction With A Speed Of 108 Km H–1. If The Muzzle Speed Of The Bullet Is 140 Ms–1, With What Speed Will The Bullet Hit The Thief’s Car?    

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Question

A police van moving on a highway with a speed of 36 km h–1 fires a bullet at a thief’s car speeding away in the same direction with a speed of 108 km h–1. If the muzzle speed of the bullet is 140 ms–1, with what speed will the bullet hit the thief’s car?    

Solution

Correct option is

120 ms–1

Speed of the police van = 36 km h–1 = 10 ms–1. Since the gun is in motion with the van and the bullet is fired in the direction in which the van is moving, the net speed of the bullet = speed of the gun (i.e., van) + the muzzle speed of the bullet = 10 + 140 = 150 ms–1. Now, the speed of the thief’s car = 108kmh–1 = 30ms–1. The bullet is chasing the thief’s car with a speed of 150 ms–1 and the thief’s car is speeding away at 30 ms–1. Hence the bullet will hit the car with a speed which is the relative speed of the bullet with respect to the car = 150 – 30 = 120 ms–1.

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