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A river is flowing from west to east with a speed $5 m s^{- 1}$ . A swimmer can swim in still water at a speed of $10 m s^{- 1}$ . If he wants to start from point $A$ on south bank and reach opposite point $B$ on north bank, in what direction should he swim?

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$30 °$ east of north

$60 °$ east of north

$30 °$ west of north

$60 °$ west of north

answer is C.

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Detailed Solution

Here, Velocity of swimmer in still water, $v_{s} = 10 m s^{- 1}$ Velocity of water flowing in river, $v_{s} = 5 m s^{- 1}$

From figure, $\sin θ = \frac{v_{r}}{v_{s}} = \frac{5}{10} = \frac{1}{2}$

$θ = \sin^{- 1} (\frac{1}{2}) = 30 °$ west of north

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