Question

Rain is falling vertically with a speed of 30 m s^-1. A woman rides a bicycle with a speed of 12 m s^-1 in east to west direction. In which direction she should hold her umbrella?

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

Answer 1

Answer: (B)

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

Answer 2

In figures, ${\overset{\rightarrow}{v}}_{r}$represent the velocity of rain and ${\overset{\rightarrow}{v}}_{b}$, the velocity of the bicycle, the woman s riding. To protect herself from rain, the woman should hold her umbrella in the directions or velocity of rain with respect to the bicycle, ${\overset{\rightarrow}{v}}_{rb}.$

$\tan\theta = \frac{v_{b}}{v_{r}} = \frac{12}{20} = \frac{2}{5}or\theta = \tan^{- 1}\left( \frac{2}{5} \right)$

Therefore, the woman should hold her umbrella at an angle of $\tan^{- 1}\left( \frac{2}{5} \right)$with the vertical towards the west.