The stream of a river is flowing with a speed of $2\: km/h$. A swimmer can swim at a speed of $4\: km/h$ . What should be the direction of the swimmer with respect to the flow of the river to cross the river straight ? Option 1) $90^{\circ}$          Option 2) $150^{\circ}$ Option 3) $120^{\circ}$ Option 4) $60^{\circ}$

$\vec{v}_{mr}=\vec{v}_{m}-\vec{r}$

$v_{m}=\vec{v}_{mr}+\vec{r}$

$\sin\theta =\frac{\left | \vec{v}_{r} \right |}{\left | v_{mr} \right |}=\frac{2}{4}=\frac{1}{2}$

$\theta =30^{\circ}$

Now, the angle with the downstream is

$=90^{\circ}+30^{\circ}$

$=120^{\circ}$

Option 1)

$90^{\circ}$

Option 2)

$150^{\circ}$

Option 3)

$120^{\circ}$

Option 4)

$60^{\circ}$

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