question_answer

A river is flowing from west to east direction with velocity v. A swimmer standing at the south bank wants to cross the river in order to reach a point just in front of the starting point. If the swimmer can swim at a speed of u w.r.t. the river flow, the angle with the north direction, required to swim is equal to

A)  \[{{\sin }^{-1}}\left[ \frac{u}{{{u}^{2}}+{{v}^{2}}} \right]\]           

B)  \[{{\sin }^{-1}}\left[ \frac{v}{{{u}^{2}}+{{v}^{2}}} \right]\]

C) \[si{{n}^{-1}}\left[ \frac{v}{u} \right]\]                  

D)  \[si{{n}^{-1}}\left[ \frac{u}{v} \right]\]

Correct Answer: C

Solution :

 Velocity of the swimmer w.r.t. the ground is the vector sum of velocity of swimmer w.r.t. the river and velocity of river w.r.t. the ground. \[Sin\,\theta =\frac{v}{u}\Rightarrow \theta ={{\sin }^{-1}}\left( \frac{v}{u} \right)\]