Rain is falling vertically downwards with a velocity of $4\, km / h$. A man walks in the rain with a velocity of $3 \,km / h$. The raindrops will fall on the man with a velocity of
- 1 km/h
- 3 km/h
- 4 km/h
- 5 km/h
The Correct Option is D
Solution and Explanation
$\vec{v}_{r m}=\vec{v}_{r}-\vec{v}_{m}$
$=4 \hat{j}-3 \hat{i}$
$=-3 \hat{i}+4 \hat{j}$
or $=5\, km/h|$
$\left|\vec{v}_{r m}\right|=\sqrt{(-3)^{2}+(4)^{2}}$
$=\sqrt{9+16}$
$=\sqrt{25}=5$
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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.
Read More: Addition of Vectors