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Let i^ and j^ be unit vector in horizontal and vertical respectively.
Let velocity of rain Vr=ai^+bj^
speed of rain = √(a^2+b^2)
When relative velocity of rain w.r.t man is vertical
Vrm = Vr−Vm
Vm = 4i^
Vrm = (a−4)i^+ bj^
Since Vrm is vertical
a−4=0 => a=4
When relative velocity is at 45∘
Vm = 8i^
Since tanθ = b/(−4)
Therefore, Speed = √(4^2+4^2) =4√2
Hence, the actual velocity of rain is 4√2 m/s