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A river is flowing from $\mathrm{W}$ to $\mathrm{E}$ 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:
$120^{\circ}$ with downstream
For shortest possible path man should swim with an angle $(90+\theta)$ with downstream. From the fig,
$\begin{aligned} & \sin \theta=\frac{v_r}{v_m}=\frac{5}{10}=\frac{1}{2} \\ & \Rightarrow \therefore \theta=30^{\circ}\end{aligned}$
So angle with downstream $=90^{\circ}+30^{\circ}=120^{\circ}$
$\begin{aligned} & \sin \theta=\frac{v_r}{v_m}=\frac{5}{10}=\frac{1}{2} \\ & \Rightarrow \therefore \theta=30^{\circ}\end{aligned}$
So angle with downstream $=90^{\circ}+30^{\circ}=120^{\circ}$
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