Question

Rain is falling vertically with a speed of `1m//s`. A woman rides a bicycle with a speed of `1.732 m//s` in east to west direction. What is the direction in which she should hold her umbrella?

Answer 1

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 here 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)=sqrt3/1 rArr theta =60^(@)`
Therefore, the woman should hold her umbrella at an angle of about `60^(@)` with the vertical towards the west