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A standing man observes rain falling wit...

A standing man observes rain falling with the velocity of `20 m s^-1` at an angle of `30^@` with the vertical.
(a) Find the velocity with which the man should move so that rain appears to fall vertically to him.
Now if he further increases his speed, rain again appears to fall at `30^@` with the vertical. Find his new velocity.

Text Solution

Verified by Experts

`vecV_(m)=-vhati("let")`
`vecV_(R)=-10hati-10sqrt3hatj`
`vecV_(RM)=-(10-v)hati-10-sqrt3hatj`
`rArr-(10-v)=0`
(for vertcal fall , horizontal component must be zero)
(or)`v=10m//s`

`vecV_(R)=-10hati-10sqrt3hatj`
`vecV_(m)=-v_(x)hati`
`vecV_(RM)=-(10-v_(x))hati-10sqrt3hatj`
Angle with the vertical =`30^(@)`
`rArr tan 30^(@)=(10-v_(x))/(10sqrt3)rArr v_(x) =20m//s`
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