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A river is flowing from west to east with a speed of $5 \mathrm{~m} / \mathrm{min}$. A man can swim in still water with a velocity $10 \mathrm{~m} / \mathrm{min}$. In which direction should the man swim so, as to take the shortest possible path to go to the south?
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The correct answer is:
$30^{\circ}$ east of south
Let the swimmer swims at an angle $\theta$ with the vertical.
$\begin{aligned} \therefore \quad \sin \theta & =\frac{v_r}{v_s}=\frac{5}{10}=\frac{1}{2}=\sin 30^{\circ} \\ \theta & =30^{\circ}\end{aligned}$
The swimmer should swim $30^{\circ}$ east of south to take the shortest possible path to go to the south.
$\begin{aligned} \therefore \quad \sin \theta & =\frac{v_r}{v_s}=\frac{5}{10}=\frac{1}{2}=\sin 30^{\circ} \\ \theta & =30^{\circ}\end{aligned}$
The swimmer should swim $30^{\circ}$ east of south to take the shortest possible path to go to the south.
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