A boat crosses a river of width 200m in the shortest time and is found to experience a drift of 100m is reaching the opposite bank. The time taken now is 't'. If the same boat is to cross the river by shortest path, the time taken to cross will be

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$\sqrt{3} t$

$\frac{2 t}{\sqrt{3}}$

answer is D.

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Detailed Solution

$t = \frac{d}{V_{BR}} - - (1)$
$\begin{array}{l} x = V_{RG} (\frac{d}{V_{BR}}) \\ 100 = V_{RG} \frac{(200)}{V_{BR}} \\ V_{BR} = 2 V_{RG} - - (2) \end{array}$
$t^{∣} = \frac{d}{\sqrt{V_{BR}^{2} - V_{RG}^{2}}}$
But $V_{RG} = \frac{V_{BR}}{2}$
Case (2)
$\begin{array}{l} t^{∣} = \frac{d}{\sqrt{V_{BR}^{2} - \frac{V_{BR}^{2}}{4}}} = \frac{d}{\sqrt{V_{BR}^{2} (1 - \frac{1}{4})}} = \frac{d}{\sqrt{\frac{3}{4} V_{BR}^{2}}} \\ t^{∣} = \frac{2 d}{\sqrt{3} V_{BR}} \Rightarrow t^{∣} = \frac{2 t}{\sqrt{3}} \end{array}$

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