question_answer

The velocity of a boat in still water is \[\eta \] times less than the velocity of flow of the river \[(\eta >1)\]. The angle with the stream direction at which the boat must move to minimize drifting is

A) \[\frac{\pi }{2}+{{\cot }^{-1}}\left( \frac{1}{\eta } \right)\]     

B) \[\frac{\pi }{2}+{{\sin }^{-1}}\left( \frac{1}{\eta } \right)\]     

C) \[{{\cos }^{-1}}\left( \frac{1}{\eta } \right)\]      

D) \[si{{n}^{-1}}\left( \frac{1}{\eta } \right)\]

Correct Answer: B

Solution :

[b] \[\overrightarrow{{{v}_{B+g}}}=\left( v+\frac{v}{\eta }\left( \cos \alpha  \right)\hat{i}+\left( \frac{v}{\eta }\sin \alpha  \right) \right)\hat{j}\] Drifting \[D=\left( v+\frac{v}{\eta }\cos \alpha  \right)\frac{D}{\left( \frac{v}{\eta }\sin \alpha  \right)}\] \[\frac{dD}{dt}=0\] We get \[\alpha =\frac{\pi }{2}+{{\sin }^{-1}}\frac{1}{\eta }\]