Question

A woman is holding an umbrella at angle ${30}^{\circ }$ with vertical with lower end towards herself, which is appropriate angle to protect her from rain for her horizontal velocity 10 m/s rightward. Then which of the following statements will be true ?

• A. Rain is falling at angle ${30}^{\circ }$ with vertical, towards the woman.
• B. Rain may be falling at angle ${30}^{\circ }$ with vertical, away from the woman.
• C. Rain may be falling vertically.
• D. None of these.

Answer 1

Answer: (B), (C)

The correct options are
B Rain may be falling at angle ${30}^{\circ }$ with vertical, away from the woman.
C Rain may be falling vertically.


$\alpha =$ angle made by velocity of rain with vertical

When direction of velocity of rain $V_R$ with vertical approaches ${90}^{\circ }$, velocity of rain w.r.t. woman $V_{RM}$ decreases and at ${90}^{\circ }$ it becomes zero, which is not possible.

Similarly, when direction of velocity of rain $V_R$ with vertical reaches $-{30}^{\circ }$, velocity of woman becomes $V_M$ as zero, which is also not possible according to question.

Hence, $\alpha$ can vary from $-{30}^{\circ }$ to ${90}^{\circ }$.