Rain is falling vertically with a speed of `1 ms^(-1)` . A woman rides a bicycle with a speed of 1.732 `ms^(-1)` in east to west direction. What is the direction in which she should hold her umbrella ?

Explanation

In Fig. `v_(r)` represents the velocity of rain and `v_(b)`, the velocity of the bicycle, the woman is riding. Both these velocities are with respect to the ground. Since the woman is riding a bicycle, the velocity of rain as experienced by

her is the velocity of rain relative to the velocity of the bicycle she is riding. That is `v_(rb) = v_(r) - v_(b)`.
This relative velocity vector as shown in Fig. makes an angle `theta` with the vertical. it is given by
`tan theta = (v_(b))/(v_(r)) = (sqrt(3))/(1) = sqrt(3) = 60^(@)`
Therefore, the woman should hold her umbrella at an angle of about `60^(@)` with the vertical towards the west.