## 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

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

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.

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?

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?

Car *A* is moving with a speed of 36 km h^{–1} on a two-lane road. Two cars*B* 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 overtake*A* before *C* does. What must be the minimum acceleration of car *B* so as to avoid an accident?

The driver of a train *A* moving at a speed of 30 ms^{–1} sights another train*B* 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?

The driver of a train *A* moving at a speed of 30 ms^{–1} sights another train*B* 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?