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# Solution - 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 - Relative Velocity in Two Dimensions

ConceptRelative Velocity in Two Dimensions

#### Question

Rain is falling vertically with a speed of 30 m s–1. A woman rides a bicycle with a speed of 10 m s–1in the north to south direction. What is the direction in which she should hold her umbrella?

#### Solution 1

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.

vecv = vec(v_r) + (-vecv_c)

Resultant, |v| = sqrt(v_(r^2)+ v_(c^2))

|v| = sqrt(30^2+10^2)

|v| = sqrt(900+100)

|v| = sqrt1000 = 10sqrt10m

tan theta = v_c/v_r = 10/30

theta = tan^(-1)(1/3)

theta = tan^(-1)(0.333) ~~18^@

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

#### Solution 2

The situation has been demonstrated in the figure below. Here vecv = 30 "ms"^(-1) is the rain velocity in vertically downward direction and vecv_c = 10 ms^(-1) is the velocity of cyclist women in horizontal plane from north N to south S.

∴Relative velocity of rain w.r,t cyclist vecv_(rc) subtends an angle β with verticle such that

tan beta = |vecv_c|/|vecv_r| = 10/30 = 1/3

:. beta = tan^(-1)(1/3) - 18^@26

Hence the woman should hold her umberlla at 18^@26 south of verticle

Is there an error in this question or solution?

#### APPEARS IN

NCERT Physics Textbook for Class 11 Part 1
Chapter 4: Motion in a Plane
Q: 12 | Page no. 86

#### Reference Material

Solution for question: 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 concept: Relative Velocity in Two Dimensions. For the courses CBSE (Arts), CBSE (Commerce), CBSE (Science)
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