question_answer

A river is flowing from west to east with a speed of 5 m/min. A man can swim in still water with a velocity 10 m/min. In which direction should the man swim so as to take the shortest possible path to go to the south?

A) \[30{}^\circ \]east of south

B) \[60{}^\circ \]east of south

C)  \[60{}^\circ \]west of south

D) \[30{}^\circ \]west of north

Correct Answer: A

Solution :

                 Let the swimmer swims at an angle\[\theta \]with the vertical from figure.                 \[\sin \theta =\frac{{{v}_{r}}}{{{v}_{b}}}\] where\[{{v}_{r}}\]is velocity of river,\[{{v}_{b}}\]is velocity of man. Given, \[{{v}_{r}}=5m/\min ,{{v}_{b}}=10m/\min \] \[\therefore \]  \[\sin \theta =\frac{5}{10}=\frac{1}{2}\] \[\Rightarrow \]               \[\theta ={{30}^{o}}\] The component\[10\text{ }sin\theta ,\]of swimmers velocity will cancel the velocity of river and the swimmer takes the shortest distance to the south. Therefore, direction is\[30{}^\circ \]east of south.