Question

Rain is falling vertically with a speed of $30m/s$. A woman rides a bicycle with a speed of $12m/s$ in east to west direction. What is the direction in which she should hold her umbrella?

• A. At an angle of ${\tan }^{-1}(\frac{2}{5})$ with the vertical towards the east
• B. At an angle of ${\tan }^{-1}(\frac{2}{5})$ with the vertical towards the west
• C. At an angle of ${\tan }^{-1}(\frac{5}{2})$ with the vertical towards the east
• D. At an angle of ${\tan }^{-1}(\frac{5}{2})$ with the vertical towards the west

Answer 1

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


In figure, $\overrightarrow{V_r}$ represents the velocity of rain and $\overrightarrow{V_b}$ represents the velocity of the bicycle with which the woman is riding. To protect herself from rain, the woman should hold her umbrella in the direction of the relative velocity of rain with respect to the bicycle i.e. $\overrightarrow{V_{rb}}$.
From the figure,
$\tan \theta =\frac{|\overrightarrow{V_b}|}{|\overrightarrow{V_r}|}=\frac{12}{30}=\frac{2}{5}$ or $\theta ={\tan }^{-1}(\frac{2}{5})$
Therefore, the woman should hold her umbrella at an angle of ${\tan }^{-1}(\frac{2}{5})$ with the vertical towards the west.