A river is flowing from west to east at a speed of $$5$$ metre per minute. A man on the south bank of the river, capable of swimming at $$10$$ metre per minute in still water, wants to swim across the river in the shortest time. He should swim in a directions:

Question

A  river is flowing from west to east at a speed of $$5$$ metre per minute. A man on  the south bank of the river, capable of swimming at $$10$$ metre per minute in  still water, wants to swim across the river in the shortest time. He should  swim in a directions:

Infinity Learn · Accepted Answer

Let  the width of the river beL     . If the man swims in a direction making an angle θ      with the bank with a  velocityV     , then the component of the velocity which helps him to  cross the river isVsinθ     . Hence, the time T      taken to cross the  river is given by:  $$T=LV$$ $$sin$$θ     For  this time T      to be minimum, $$sin$$θ      should be maximum,i.e.,  $$sin$$θ$$=+1$$     θ$$=900$$     Hence,  the man should swim due north.

A river is flowing from west to east at a speed of 5 metre per minute. A man on the south bank of the river, capable of swimming at 10 metre per minute in still water, wants to swim across the river in the shortest time. He should swim in a directions:

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