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

Infinity Learn · Accepted Answer

Refer  to 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 $$river=w$$υ$$cos$$θ     .This time is the shortest if θ$$=00$$     . Hence the man should swim in the north direction.

A river is flowing from west to east at a speed of $5 \frac{m}{\min u t e}$ . In what direction should a man on the south bank of the river capable of swimming at $10 \frac{m}{minute}$ in still water swim to cross the river in the shortest time?

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

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

A river is flowing from west to east at a speed of $5 \frac{m}{\min u t e}$ . In what direction should a man on the south bank of the river capable of swimming at $10 \frac{m}{minute}$ in still water swim to cross the river in the shortest time?