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?
Figure showing the directions of velocities of rain and cycle
Explanation: Direction in which the umbrella should be held is opposite to the direction of velocity of rain with respect to cycle.
Vr = Velocity of rain
Vc = Velocity of cycle
Velocity of rain w.r.t the cycle = Vrc = Vr-Vc
= 30 m/s + (-10)m/s
= 20 m/s
= 0.33
θ = tan-1(0.33)
= 18.26˚
Hence, the woman must hold the umbrella towards the south at an angle of 18.26˚ to the vertical direction.
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