Rain is falling vertically with a speed of 1ms^(-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 ?

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 1.732 ms^(-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 `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.