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  4. 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 ms-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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Q. 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 $10\,ms^{-1}$.
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?Physics Question Image

Motion in a Plane

Solution:

image
Here, Velocity of swimmer in still water,
$v_s = 10 \,ms^{-1}$
Velocity of water flowing in river,
$v_r = 5 \,m s^{-1}$
From figure,
$sin\,\theta=\frac{v_{r}}{v_{s}}=\frac{5}{10}=\frac{1}{2}$
$\theta=sin^{-1}\left(\frac{1}{2}\right)$
$=30^{°}$ west of north