Rain is falling vertically with a speed of 30 | vedclass

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Question

(B) Let $v_r$ be the velocity of the rain falling vertically downwards,$v_r = 30\; m/s$.Let $v_c$ be the velocity of the cyclist moving from north to

Vedclass · Accepted Answer

$	heta=	an ^{-1}\left(\frac{1}{3}ight)$

Vedclass · Answer

(B) Let $v_r$ be the velocity of the rain falling vertically downwards,$v_r = 30\; m/s$.Let $v_c$ be the velocity of the cyclist moving from north to south,$v_c = 10\; m/s$.The relative velocity of the rain with respect to the woman is given by $\vec{v}_{rw} = \vec{v}_r - \vec{v}_c$.To protect herself from the rain,the woman must hold her umbrella in the direction of the relative velocity $\vec{v}_{rw}$.The angle $	heta$ that the relative velocity vector makes with the vertical is given by:$	an 	heta = \frac{|\vec{v}_c|}{|\vec{v}_r|} = \frac{10}{30} = \frac{1}{3}$.Therefore,$	heta = 	an^{-1}\left(\frac{1}{3}ight)$.The woman should hold her umbrella at an angle of $	an^{-1}\left(\frac{1}{3}ight)$ with the vertical towards the south.

Rain is falling vertically with a speed of $30\; m/s$. $A$ woman rides a bicycle with a speed of $10\; m/s$ in the north to south direction. What is the direction in which she should hold her umbrella?

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