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

Rain is falling vertically with a speed of 1ms^(-1). A woman rides a b

1.	Rain is falling vertically with a speed of 1ms^(-1). A woman rides a bicycle with a speed of 1.732ms^(-1) in east to west direction. What is the direction in which she should hold her umbrella?
Answer» Solution :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 `tantheta=(v_(b))/(v_(r))=(sqrt(3))/(1)=sqrt(3)=60^(@)` Therefore, the woman should HOLD her umbrella at an angle of about `60^(@)` WIHT the vertical TOWARDS the west.