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).