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Rain is falling vertically with a speed ...

Rain is falling vertically with a speed of 20 m/s relative to air. A person is running in the rain with a velocity of 5 m/s and a wind is also blowing with a speed of 15 m/s (both towards east). Find the angle with the vertical at which the person should hold his umbrella for best protection from rain

Text Solution

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`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`
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