## Question

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?

### Solution

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 *v _{w}* of water. It follows from the figure that

= 25 – 9

= 16

.

#### SIMILAR QUESTIONS

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