• # question_answer 16) A boat crosses a river from port A to port B, which are just on the opposite side. The speed of the water is ${{V}_{W}}$ and that of boat is ${{V}_{B}}$ relative to still water. Assume${{V}_{B}}=2{{V}_{W}}$. What is the time taken by the boat, if it has to cross the river directly on the AB line? A) $\frac{2D}{{{V}_{B}}\sqrt{3}}$                      B) $\frac{\sqrt{3}D}{2{{V}_{B}}}$C) $\frac{D}{{{V}_{B}}\sqrt{2}}$                        D) $\frac{D\sqrt{2}}{{{V}_{B}}}$

Solution :

From figure, ${{V}_{B}}\text{ }sin\,\theta \,\,=\,\,{{V}_{W}}$   $\sin \,\theta \,=\,\frac{{{V}_{W}}}{{{V}_{B}}}\,=\,\frac{1}{2}\,\,\Rightarrow \,\,\theta =30{}^\circ \,\,\,\,\,\,\,\,\,\,[\because \,\,{{V}_{B}}=2{{V}_{W}}]$ Time taken to cross the river, $t=\frac{D}{{{V}_{B}}\cos \,\theta }=\frac{D}{{{V}_{B}}\,\cos \,30{}^\circ }=\frac{2D}{{{V}_{B}}\,\sqrt{3}}$

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