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(D) Let $\vec{V}_r$ be the velocity of rain and $\vec{V}_m$ be the velocity of the man.When the man is running,the relative velocity of rain with resp

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$\frac{10}{\sqrt{3}}\,m/s$

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(D) Let $\vec{V}_r$ be the velocity of rain and $\vec{V}_m$ be the velocity of the man.When the man is running,the relative velocity of rain with respect to the man is $\vec{V}_{rm} = \vec{V}_r - \vec{V}_m$. Given that this is vertical,$\vec{V}_{rm} = -10\hat{j}$.Thus,$\vec{V}_r - \vec{V}_m = -10\hat{j}$,which implies $\vec{V}_r = \vec{V}_m - 10\hat{j}$.Since the man is running horizontally,let $\vec{V}_m = v\hat{i}$. So,$\vec{V}_r = v\hat{i} - 10\hat{j}$.When the man stops,he observes the actual velocity of the rain $\vec{V}_r$,which makes an angle of $30^o$ with the vertical.From the components of $\vec{V}_r$,$	an 30^o = \frac{|v_x|}{|v_y|} = \frac{v}{10}$.Therefore,$v = 10 	an 30^o = 10 	imes \frac{1}{\sqrt{3}} = \frac{10}{\sqrt{3}}\,m/s$.

$A$ person running horizontally observes that rain is falling on his head vertically with a speed of $10\,m/s$. When he stops,he observes that the rain is falling at an angle of $30^o$ with the vertical. Find the speed with which the man was running.

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