Rain is falling vertically with a speed of ` 30 ms^(-1)` . A woman rides a bicycle with a speed of ` 10 ms^(-1)` in the North to South direction. What is the direction in which she should hold her umbrella ?

Explanation

In Fig . 4.16 `v_(r )` represents the velocity of rain and `v_(b)` , the velocity of the bicycle , the women 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 . 4.16 makes an angle `theta` with the vertical . It is given by
`tantheta=(v_(b))/(v_(r))=(12)/(35)=0.343``tantheta=(v_(b))/(v_(r))=(12)/(35)=0.343`
Or , `theta~=19^(@)`
Therefore , the women should hold her umbrella at an angle of about `19^(@)` with the vertical towards the west .