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A man is moving due east with a speed 1 ...

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.

Text Solution

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`tan theta=(1)/(sqrt(3)), theta=30^(@)`
`overset(vec)V_(M)=(1" kmhr"^(-1))hati`
`overset(vec)V_(R )=(sqrt(3)"kmhr"^(-1))(-hatj)`
`overset(vec)V_(RM)=overset(vec)V_(R )-overset(vec)V_(M)=(-sqrt(3)hatj-hati)`
`|overset(vec)V_(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.
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