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A man can swim in still water at a speed of 3 km/h. He wants to cross a river that flows at 2 km/h and reach the point directly opposite to his starting point. How much time will he take to cross the river if the river is 500 m wide?

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$\frac{\sqrt{5}}{10} h$

$\frac{\sqrt{6}}{10} h$

$\frac{\sqrt{7}}{10} h$

$\frac{\sqrt{8}}{10} h$

answer is A.

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Detailed Solution

$\begin{array}{l} sinθ = \frac{2}{3} \Rightarrow cosθ = \frac{\sqrt{5}}{3} \\ t = \frac{d}{vcosθ} = \frac{0.500}{3 cosθ} = \frac{\sqrt{5}}{10} hr \end{array}$

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