Question

A swimmer can swim in still water with speed $v$ and the river flowing with velocity $\frac{v}{2}$. To cross the river in shortest distance, he should swim making an angle $\theta$ with the upstream. What is the ratio of the time taken to swim across in the shortest time to that in swimming across over shortest distance?

• A. $\sin \theta$
• B. $\cos \theta$
• C. $\tan \theta$
• D. $\cot \theta$

Answer 1

The correct option is A $\sin \theta$

For shortest distance , Time taken $=\frac{W}{V_{b}sin\theta }$
For shortest time , Time taken $=\frac{W}{V_b}$
Ratio of times taken for shortest time to that of shortest path $=\frac{\frac{W}{V_b}}{\frac{W}{V_{b}sin\theta }}=sin\theta$