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The statement "If a man is travelling on a road with a speed of 6m/s. Suddenly rain starts and falls on his head vertically downward. " implies that the rain has a horizontal component of 6 m/s in the same direction the runner is running. When he runs at the same speed, the rain apears to come straight down. 

If he increases his speed to 12 m/s, there is a 6m/s relative velocity of wind into his face in horizontal direction. Furthermore, the rain now falls at the angle of 60 degree with vertical

 

The vertical component of the wind velcity, Vy, must such that 6/Vy = tan 60 
Vy = 3.464 m/s
Vx = 6.00 m/s
Wind speed (magnitude) = 6.93 m/s