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

Question

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

Infinity Learn · Accepted Answer

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 υ$$cos$$θ , where θ is the angle between the north direction and the direction of velocity v.∴  Time taken to cross the river $$=$$ wυ$$cos$$θ .This time is the shortest if θ$$=00$$ . Hence the man should swim in the north direction, which is choice $$4$$.

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

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