Question:

Rain is falling vertically with a speed of 12 ms−112 \,ms^{-1}. A woman rides a bicycles with a speed of 12 ms−112 \,ms^{-1} in east to west direction. What is the direction in which she should hold her umbrella?

Updated On: Sep 13, 2024
  • 30∘30^\circ towards East
  • 45∘45^\circ towards East
  • 30∘30^\circ towards West
  • 45∘45^\circ towards West
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The Correct Option is D

Solution and Explanation

To protect herself from the rain, the woman must hold her umbrella in the direction of the relative velocity of the rain with respect to the woman.
tan⁡ θ=vw/vf=12 m/s\tan\, \theta= v _{ w } / v _{ f }=12\, m / s
or, tan⁡ θ=1\tan \,\theta=1
or, θ=45∘\theta=45^{\circ}
Therefore, the direction in which she should hold her umbrella is 45∘45^{\circ} toward west.
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Concepts Used:

Addition of Vectors

A physical quantity, represented both in magnitude and direction can be called a vector.

For the supplemental purposes of these vectors, there are two laws that are as follows;

  • Triangle law of vector addition
  • Parallelogram law of vector addition

Properties of Vector Addition:

  • Commutative in nature -

It means that if we have any two vectors a and b, then for them

a→+b→=b→+a→\overrightarrow{a}+\overrightarrow{b}=\overrightarrow{b}+\overrightarrow{a}

  • Associative in nature -

It means that if we have any three vectors namely a, b and c.

(a→+b→)+c→=a→+(b→+c→)(\overrightarrow{a}+\overrightarrow{b})+\overrightarrow{c}=\overrightarrow{a}+(\overrightarrow{b}+\overrightarrow{c})

  • The Additive identity is another name for a zero vector in vector addition.

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