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

The woman should hold the umbrella in a direction of relative velocity of rain . W.r.t woman .

The relative velocity of rain w.r.t woman is represent by the diagonal of the parallelogram ABCD .
The direction with the vertical is given by In triangle ABC
`tan theta =10//30 `
`theta =tan ^(-1) (1)/(3)`
or `theta =18^(@) 26`.
Thus the woman should hold her umbrella at an angle of about `18^(@)` with the vertical, towards the south .