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A person reaches a point directly opposite on the other bank of a river. The velocity of the water in the river is 4 m/s and the velocity of the person in still water is 5 m/s. If the width of the river is 84.6m, time taken to cross the river in seconds is

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28.2

84.6

9.4

answer is D.

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Detailed Solution

$vsin θ = v_{river} \Rightarrow sinθ = \frac{4}{5}$

Thus net velocity of man in the direction of crossing $= vcosθ = 5 m / s \times \frac{3}{5} = 3 m / s$

Thus total time taken to cross the river $= \frac{84.6 m}{3 m / s} = 28.2 s$

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