Question

A river is flowing from west to east at a speed of 5 m/min. A man on the south bank of the river, capable of swimming at 10 m/min in still water, wants to swim across the river in the shortest time. Finally, he will swim in a direction

A
tan1(B) E of N
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B
tan1(B) N of E
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C
30 E of N
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D
60 E of N
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Solution

The correct option is C 30∘ E of NWe have,River speed =5m/minAnd Man speed =10m/minSo,Let the width of river =xmtrHe travels due north then his rtesultant velocity acts 30 degree north of east and the distance to be covered to reach the other bank increase to xcos30oAnd resultant velociity =11.2m/minSo time taken x9.7mins If the travels due 30 degree north of east then his resultant velocity (Due to velocity of downstream of water ) acts due north.The distance be covered to reach the other bank will be x mtrs.And the resultant velocity is 8.7mtr/min.So time taken is x8.7mins.Then, 30 degree east of northSo at least time he should travel due to north.Hence, this is the answer.

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