Rain is falling vertically with a speed of ` 10 sqrt 3 ms^(-1)`. A woman rides a bicycle with a speed of ` 10 ms^(-1)` in east to west direction. What is the derection in which she shold hold her umbrella to protect from rain ?

Explanation

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 rains as experienced by

her in the velocity of rain relative to th 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) = 12/35 = 0.343` ltrbgt Or, `theta=19^(@)`
Therefore, the woman should hold the umbrella at an angle of about `19^(@)` with the vertical towards the west.