Let velocity of man V1 = 10i

velocity of rain drop Vo = ai + bj

consider vertically downward direction as positive.

Vo1 = ai + bj - 10i

= (a-10)i + bj

raindrops appears to fall in vertical direction . hence X - component is zero

a-10 = 0

a = 10

in second case

V2 = 20i

Vo2 = 10i + bj - 20i

= -10i + bj

raindrops appears to fall in the direction making an angle 30 with vertical

tan 120 = -10 / b (angle is measured from positive X-axis 90 + 30 = 120)

-√3 = -10/b

b = 10/√3

hence velocity of raindrops w.r.t. ground Vo = 10i + 10j/√3

speed of raindrops w.r.t. ground = √{10² + (10/√3)²}

= √(100+100/3)

= 20/√3

direction tanα = (10/√3)/10

= 1/√3

α = 30 w.r.t. ground.