A 120 Metre Long Train Is Moving West At A Speed Of 10 Ms–1. A Small Bird Flying East At A Speed Of 5 Ms–1 crosses The Train. What Is The Time Taken By The Bird To Across The Train?

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?    

Rain is falling vertically with a speed of 4 ms^–1. After some time, wind starts blowing with a speed of 3 ms^–1 in the north to south direction. In order to protect himself from rain, a man standing on the ground should hold his umbrella at an angle  given by

A swimmer can swim in still water with a speed of 5 ms^–1. While crossing a river his average speed is 3 ms^–1. If he crosses the river in the shortest possible time, what is the speed of flow of water?