Rain is falling vertically with a speed fo `35 ms^(-1)`. Winds starts blowing after sometime with the speeds of `12ms^(-1)` in east to west direction. At what angles with the vertical should a boy waiting at a bus stop hold his umbrella to protect himself from rain?

Explanation

Refer to Fig. 2 (c ) . 53,
.
` vec v_r = vec (OA) = 35 ms(-10`, along vertical
` vec v_b = vec (OB) = 12 ms^(-1)` along West, The womman Can protect herself from the rain if she holds her umbrella in the direction of relative of rain w.r.t. bicycle, To find the relatice velocity of rain w.r.t. bicycle, bring the bicycyle at rest by impositn a velocit ` -vec v_b9= vec (OC) on bicycle an apply this velocity on rain also. Now the relative velocity of rain w.r.t. bicycyle ` vec (v_(rb))` will be the resultant of ` vec v-r (= vec (OA)) and -vec v_b (= vec (OC)) , which will be represented by diagonal ` vec (OD)` of rectangle ` OADC`.
` tan theta = (AD)/(OA) = v_b/v_r =(12)/935) = 0.3429 = tan 18^@ 56'`
` theta = 18^@ 56'` with the vertial towards the West.