A river flows from west to east at a speed of 5 metres per minute. A man on the south bank, who can swim at 10 metres per minute in still water, wishes to cross the river in the shortest time. In which direction should he swim?

Step-by-step solution

Let the width of the river be d . The velocity of the man in still water is v_ m = 10 m/min and the velocity of the river is v_ r = 5 m/min. Let the man swim at an angle with respect to the direction perpendicular to the river flow (due north). The component of the man's velocity perpendicular to the river flow is v_ m . The time taken to cross the river is given by t = d v_ m . To minimize the time t , the component v_ m must be maximum. The maximum value of is 1 , which occurs when = 0^ . Therefore, the man shoul