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 Fig. 2 (c ).51, ltbr. ` vec V_w = vec (OB) =12 ms^(-1)`, along West
` vec v _r = vec (OA) =35 ms^-1)`,
along vertical downward
The boy can protect himself from the rain of he holds his umbrella in the direction of resultant
velocity` vec R or vec v-r and vec v_w`, i,e, along the direction ` OC` as shown in Fing. 2 9c ) .51. If ` theta` is the angle wich ` vec R` makes with the vertical direfction, then
.
` tan theta = v-w/v-r = (12)/(35) =0 . 3429 = tan18^@ 56'`
:. ` theta = 18^@ 56'` with vertical towards East.