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.

SIMILAR QUESTIONS

Q1

A man can swim at a speed of 3 km/hr in still water. He wants to cross a 500 m wide river flowing at 2 km/hr. He keeps himself always at angle of 120o with the river flow when swimming find the time he takes to cross the river.

Q2

A train is moving southwards at a speed of 30 ms–1. A monkey is running northwards on the roof of the train with a speed of 5ms–1. What is the velocity of the monkey as obserced by a person standing on the ground?

Q3

A jet airplane traveling from east to west at a speed of 500 kmh–1 ejects out gases of combustion at a speed of 1500 kmh–1 with respect to the jet plane. What is the velocity of the gases with respect to an observer on the ground?   

 

Q4

Car A is moving with a speed of 36 km h–1 on a two-lane road. Two carsB and C, each moving with a speed of 54 km h–1 in opposite direction on the other lane are approaching car A. At a certain instant when the distance AB = distance AC = 1 km, the diver of car B decides to overtakeA before C does. What must be the minimum acceleration of car B so as to avoid an accident?   

Q5

The driver of a train A moving at a speed of 30 ms–1 sights another trainB moving on the same track at a speed of 10 ms–1 in the same direction. He immediately applies brakes and achieves a uniform retardation of 2 ms–1. To avoid collision, what must be the minimum distance between the trains?      

Q6

The driver of a train A moving at a speed of 30 ms–1 sights another trainB moving on the same tack towards his train at a speed of 10 ms–1. He immediately applies brakes and achieves a uniform retardation of 4 ms–2. To avoid head-on collision, what must be the minimum distance between the trains?