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.

Explanation

` vecV_(R) =- 10 hati - 10 sqrt(3) hatj`
` vecV_m =- v_x hati`
` vecV_(RM) =- (10 - v_x) hati - 10 sqrt(3) hatj `
Angle with the vertical `=30^@`
` implies tan 30^@ =( 10 -v_s )/( - 10 sqrt( 3)) implies v_x = 20 m//s`