Question

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.

Answer 1

`tan theta=(1)/sqrt(3), theta=30^(@)`
`vecv_(M)=(1km hr^(-1))hati vecv_(R)=(sqrt(3) kmhr^(-1))(-hatj)`
`vecv_(RM)=vecv_(R)-vecV_(M)=(-sqrt(3)hatj-hati) |vecv_(RM)|=sqrt((sqrt(3))^(2)+1^(2))=2 km hr^(-1)`
Angle of relative velocity with vertical is `30^(@)` so that man has to tilt his umbrella at `30^(@)` with vertical towards the east