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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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`vec(V_("Rain"))=vec(V_(R))=20(-hat(K))`
`vec(V_("Man"))=vec(V_(M))=5hat(i)`
`vec(V_(wind))=vec(V_(W))=15hat(i)`
Resultant velocity of rain and wind =
`vec(V_(RM))=-20hat(K)+15hat(i)`
Now, Velocity of Rain relative to man=
`vec(V_(RM))-vec(V_(M))`
`=(-20hat(K)+15hat(i))-(5hat(i))`
`=-20hat(K)+10hat(i)`
`Tanalpha==(1)/(2)rArr alpha = Tan^(-1)(1)/(2)`
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