• question_answer A boat crosses a river from point A to point B, which are on opposite sides. The speed of water is v and that of boat is ${{v}_{w}}$relative to still water. Assume${{v}_{B}}=2{{v}_{w}}.$What is the time taken by the boat to cross the river, if the width of the river is D A) $\frac{2D}{{{v}_{B}}\sqrt{3}}$                 B) $\frac{\sqrt{3}D}{2{{v}_{B}}}$     C)               $\frac{D}{{{v}_{B}}\sqrt{2}}$       D)   $\frac{D\sqrt{2}}{{{v}_{B}}}$

Correct Answer: A

Solution :

Where b is the velocity of boat with respect to ground Let the time to cross the river bet t $t=\frac{D}{v}=\frac{D}{\sqrt{v_{B}^{2}-v_{w}^{2}}}=\frac{D}{\sqrt{v_{B}^{2}-{{\left( \frac{{{v}_{B}}}{2} \right)}^{2}}}}$ $\therefore$    $t=\frac{2D}{{{v}_{B}}\sqrt{3}}$ Hence, the correction option is (a).

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