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. vr represents the velocity of rain and v , 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_(t)-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.