Question

Question 4.12 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?

Chapter Motion In A Plane Page 86

Answer 1

Rain is falling vertically downward with speed ( Vr)= 30(-j) m/s .

Woman ride bicycle with speed of 10m/s in the North to South direction .e.g Vw = 10(i) m/s (North to South )

See the figure ,
For protection herself form the rain , woman should hold her umbrella in the direction of relative velocity of rain with respect to woman.

e.g Vrw = Vr - Vw
= -30j - 10i
So, |Vrw| = √(30² + 10²)
= 10√10m/s

And angle makes with vertical is ∅

Then , cos∅ = |(-30j- 10i).(j)|/10√10 = 3/√10
∅ = cos-¹(3/√10)
Hence, woman should hold her umbrella at an angle of cos-¹(3/√10) with vertical, towards South.

Answer 2

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The described situation is shown in the attached file.... please see them!!

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 = v r + (-v c )

=30+(-10)

=20 m/s

tanθ = v c/ v r = 10/30

=> Θ = tan^-1(1/3)= tan^-1 (0.333) = 18 degree

Hence, the woman must hold the umbrella toward the south, at an angle of nearly 18° with the vertical.

I hope, this will help you

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