A river is flowing from west to east at a speed of 5 metre per minute. A man on the south bank of the river, capable of swimming at 10 metre per minute in still water, wants to swim across the river in the shortest time. He should swim in a directions:

Let the width of the river beL . If the man swims in a direction making an angle θ  with the bank with a velocityV , then the component of the velocity which helps him to cross the river isVsinθ . Hence, the time T  taken to cross the river is given by: T=LV sinθ For this time T  to be minimum, sinθ  should be maximum,i.e., sinθ=+1 θ=900 Hence, the man should swim due north.