Rain is falling vertically with a speed of `30 ms^-1`. A woman rides a bicycle with a speed of `10 m s^-1` in the north to south direction. What is the direction in which she should hold her umbrella ?

Explanation

In order to protect from rain, woman should hold her umberalla in the direction of relative velocity of rain w.r.t. women i.e., `v _(rw)`
Here `tan beta = ( v _(w))/( v _(r)) = (10)/(30) implies tan beta = (1)/(3)`
`beta = tan ^(-1) ((1)/(3)) = beta = 18 ^(@) 26`
So, woman should hold her umbrela at an angle of `18^(@)26.` wth the vertical, towards south.