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 situation has been demonstrated in the figure below. Here `vecv_(r)=30ms^(-1)` is the rain velocity in vertically downward direction and `vec_(c) = 10ms^(-1)` is the velocity of cyclist woman in horizontal plane from north N to south S.
`therefore` Relative velocity of rain w.r.t cyclist `vec_(rc)` subtends an angle `beta` with vertical such that
`tan beta = |vecc/vecv_(r)|= 10/[30=1/3`
`beta = tan^(-1)(1/3)= 18^(@)26^(')`
Hence, the woman should hold her umbrella at `18^(@)` `26^(')` south of vertical.