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

Explanation

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