Rain is falling vertically with a speed of 30 | vedclass

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(B) Let the velocity of rain be $\vec{v}_r = -30\hat{j}\,ms^{-1}$ and the velocity of the bicycle be $\vec{v}_b = -12\hat{i}\,ms^{-1}$ (since she is m

Vedclass · Accepted Answer

At an angle of $tan^{-1} (\frac {2}{5})$ with the vertical towards the west

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(B) Let the velocity of rain be $\vec{v}_r = -30\hat{j}\,ms^{-1}$ and the velocity of the bicycle be $\vec{v}_b = -12\hat{i}\,ms^{-1}$ (since she is moving from east to west).The relative velocity of rain with respect to the woman is $\vec{v}_{rb} = \vec{v}_r - \vec{v}_b = -30\hat{j} - (-12\hat{i}) = 12\hat{i} - 30\hat{j}\,ms^{-1}$.To protect herself from rain,she must hold the umbrella in the direction of the relative velocity of rain $\vec{v}_{rb}$.The angle $	heta$ with the vertical is given by $	an 	heta = \frac{|v_b|}{|v_r|} = \frac{12}{30} = \frac{2}{5}$.Thus,$	heta = 	an^{-1}(\frac{2}{5})$.Since the relative velocity vector has a positive $x$-component (eastward relative to the woman) and a negative $y$-component (downward),the rain appears to come from the east. Therefore,she must tilt her umbrella towards the west to block the rain.

Rain is falling vertically with a speed of $30\,ms^{-1}$. $A$ woman rides a bicycle with a speed of $12\,ms^{-1}$ in the east to west direction. She should hold her umbrella:

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