Question:
Rain is falling vertically with a speed of $12 \,ms^{-1}$. A woman rides a bicycles with a speed of $12 \,ms^{-1}$ in east to west direction. What is the direction in which she should hold her umbrella?
Rain is falling vertically with a speed of $12 \,ms^{-1}$. A woman rides a bicycles with a speed of $12 \,ms^{-1}$ in east to west direction. What is the direction in which she should hold her umbrella?
Updated On: Sep 13, 2024
- $30^\circ$ towards East
- $45^\circ$ towards East
- $30^\circ$ towards West
- $45^\circ$ 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.
$\tan\, \theta= v _{ w } / v _{ f }=12\, m / s$
or, $\tan \,\theta=1$
or, $\theta=45^{\circ}$
Therefore, the direction in which she should hold her umbrella is $45^{\circ}$ toward west.
$\tan\, \theta= v _{ w } / v _{ f }=12\, m / s$
or, $\tan \,\theta=1$
or, $\theta=45^{\circ}$
Therefore, the direction in which she should hold her umbrella is $45^{\circ}$ 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
\(\overrightarrow{a}+\overrightarrow{b}=\overrightarrow{b}+\overrightarrow{a}\)
- Associative in nature -
It means that if we have any three vectors namely a, b and c.
\((\overrightarrow{a}+\overrightarrow{b})+\overrightarrow{c}=\overrightarrow{a}+(\overrightarrow{b}+\overrightarrow{c})\)
- The Additive identity is another name for a zero vector in vector addition.
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