Rain is falling vertically with a speed of 20 `ms^(-1)` A person is running in the rain with a velocity of 5 `ms^(-1)` and a wind is also blowing with a speed of 15 `ms^(-1)`. (both from the west). The angle with the vertical at which the person should hold his umbrella so that he may not get drenched is:

Explanation

`vecV_("rain") =vecV_(R) =20(-hatk)`
`vecV_("man") =vecV_(M) =5hati` `V_("wind") =vecV_(W) =15hati`
Resultant velocity of rain and wind = `vecV_(RM) =-20vecK + 15hati`
Now, Velocity of Rain relative to man= `vecV_(RM) -vecV_(M) = (-20 hatK +15 hati)-(5hati)`
`=-20hatK + 10hati`
`tan alpha =1/2 rArr alpha =tan^(-1) 1/2`