The described situation is shown in the given figure.
Here,
vc = Velocity of the cyclist
vr = Velocity of falling rain
In order to protect herself from the rain, the woman must hold her umbrella in the direction of the relative velocity (v) of the rain with respect to the woman.
v = vr + (-vc)
= 30 + (-10) = 20 m/s
tan θ =
θ = tan-1
