Let i^ and j^ be unit vector in horizontal and vertical respectively.
Let velocity of rain vr=ai^+bj^
speed of rain= √a2+b2
when relative velocity of rain w.r.t man is vertical
Vrm means how man sees the velocity of rain.
Vrm = Vr – Vm
Vm = 10 i
Vrm = (a i+ b j)- 10 i
= (a-10)i + b j
Since Vrm is vertical, the horizontal component is zero.
so, a-10 = 0, a= 10
when relative velocity is at 60′
Vm = 20 i
Vrm = (a-20) i + b j
= -10 i + b j
And tan theta = b/ a = b/ -10
tan 60′ = √3 = b/ -10
so, b = -10*√3
Now we have both the a and b value, so, let’s count velocity of rain = √a2 + b2
= √(10)2 +(-10√3)2
= √400 = 20 m/s