A man is moving due east with a speed 1 km/hr and rain is falling vertically with a speed `sqrt(3)` km/hr. At what angle from vertical the man has to hold his umbrella to keep the rain away. Also find the speed of rain drops w.r.t. man.

Explanation

`tan theta =1/sqrt3 , theta=30^@`
`vecv_m=(1"km hr"^(-1))hati`
`vecv_(R) = (sqrt3 " km hr"^(-1)) (-hatj)`
`vecv_("Rm") =vecv_(R) - vecv_M=(-sqrt3 hatj - hati)`
`|vecv_("Rm")|=sqrt((sqrt3)^2+(1)^2)=2 "km hr "^(-1)`
Angle of relative velocity with vertical is `30^@` with vertical towards the east.