A river flows from west to east at a speed of . There is a man on the south bank of the river who can swim to a speed of
in calm water and wants to swim across the river in the minimum time. He must swim in one direction:
Due north
east to north
west to north.
east to north
Let the time is taken to cross the river be t.
For the time t to be minimum should be maximum,
should be 0
Therefore, swimmer should swim due north.