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

The velocity of the rain and the wind are represented by the vector `v_(r)` and `v_(w)` is R as shown in the figure. The magnitude of R is
`R= sqrt(v_(r)^(2)+v_(w)^(2)) = sqrt((35)^(2)+(12)^(2)) ms^(-1) = 37 ms^(-1)`.
The direction `theta` that R makes with the vertical is given by
`tantheta = v_(w)/v_(r) = 12/35 = 0.343`
Or, `theta = tan^(-1)(0.343)=19^(@)`.
Therefore, the boy should hold his umbrella in the vertical plane at an angle of about`19^(@)` with the vertical towards the east.