Q.12:- Rain is falling vertically with a speed of 30 m s-1. A woman rides a bicycle with a speed of 10 m s-1 in the north to south direction. What is the direction in which she should hold her umbrella ?
The described situation is shown in the given figure.
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 = vc / vr = 10 / 30
θ = tan-1 (1 / 3)
= tan-1 (0.333) ≈ 180
Hence, the woman must hold the umbrella toward the south, at an angle of nearly 18° with the vertical.