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?
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.
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 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?
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?
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?