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

Refer to Fig. 2 (c ) .72,
` velocity of rain, ` vec v_(r) = vec (OA)`,
where ` v_(r) = 10 sqrt 3 m//s`
.
velocity of bocycle, ` vec v _(b) = vec (OB)`,
where ` v_(B) =10 ms^(-1)`
In order to protect form the rain, the woman should bold the munbrella in the drection of relative velocty of rain w.r.t. bicycle [i.e. vec v_(ab)` repersented by ` vec (OP)]`.
` tan theta =(v_(b)/v_(r) =(10)/(10 dqrt 3) = 1/3 =tan 30^(@) or theta =30^(@)`
Thus the woman should hold her numbrella in the derction of ` 30^(@) with the vertical towards the west.