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?


Correct option is

4 ms–1


In order to cross the river in the shortest time, the resultant velocity v of the swimmer must be perpendicular to the velocity vw of water. It follows from the figure that 



                = 25 – 9

                = 16




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?


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