A river is flowing from west to east at a speed of 5 m/minute. In what direction should a man on the south bank of the river capable of swimming at 10 m/minute in still water swim to cross the river in the shortest time

Refer the figure. Where u is velocity of water current. Let v be the velocity of the man and let AB = w be the width of the river. The river is crossed with a velocity equal to the component of v along AB, which is υcosθ , where θ is the angle between the north direction and the direction of velocity v.∴  Time taken to cross the river = wυcosθ .This time is the shortest if θ=00 . Hence the man should swim in the north direction, which is choice 4.