Question

A river is flowing from west to east with a speed of $5mmi{n}^{-1}$. A man can swim in still water with a velocity $10mmi{n}^{-1}$. In which direction should the man swim so as to take the shortest possible path to go to the south?

• A. ${30}^o$ east of south
• B. ${30}^o$ west of south
• C. South
• D. ${30}^o$ west of north

Answer 1

Answer: (B)

${30}^o$ west of south

Here $m=man,g=ground\&r=river$
Shortest path would be $PQ$
as resultant, $\overrightarrow{v_{mr}}=\overrightarrow{v_{rg}}+\overrightarrow{v_{mg}}$ we have along west-east direction $v_{rg}=v_{mg}\sin \theta$
$\sin \theta =\frac{5}{10}or\theta ={30}^o$
So man should swim in $\theta ={30}^o$ west of south direction