The Question is from neet-physics motion-in-a-plane addition-subtraction-and-resolution-of-vectors, and it was created by the author ABDUL JILANI BASHA

Question

One of the rectangular components of a velocity of $60\,\,km{h^{ - 1\,\,\,}}\,{\rm{is}}\,\,\,30\,\,km{h^{ - 1}}$ .The other rectangular component is

ABDUL JILANI BASHA · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
	**Primary Concept**: Vector Resolution
	**Related Topics**: Vector components, Pythagorean theorem
	**Prerequisites**: Basic trigonometry, knowledge of vectors
## SOLUTION PATHWAY
**Given Information**:
	Resultant velocity: $v = 60 \,km/h$
	One component velocity: $v_1 = 30 \,km/h$
	We need to find: $v_2$
	Important condition: The components are rectangular, i.e., they are perpendicular to each other.
**Method & Steps**:
	1.	Use the Pythagorean theorem to find the magnitude of the other component.
		Reasoning: Since the components are rectangular, they form the sides of a right triangle, and the resultant vector is the hypotenuse.
		Formula/Rule: $v^2 = v_1^2 + v_2^2$
	2.	Solve for $v_2$.
		Working: $v_2^2 = v^2 - v_1^2$
		$v_2^2 = 60^2 - 30^2 = 3600 - 900 = 2700$
		$v_2 = \sqrt{2700} = \sqrt{900 	imes 3} = 30\sqrt{3}$ km/h
		Key Point: Remember to take the square root to find the magnitude of the component.
	3.	State the answer.
		Result: The other component is $30\sqrt{3} \,km/h$.
		Verification: $30^2 + (30\sqrt{3})^2 = 900 + 2700 = 3600 = 60^2$. The Pythagorean theorem holds true.
 ## OPTION ANALYSIS
[A] :x: Incorrect, this would be true if both components were equal.
[B] ✓: Correct, this is the result of the calculation.
[C] :x: Incorrect, this would be true if the resultant vector was 60$\sqrt{2}$ and components were equal.
[D] :x: Incorrect, the resultant vector would be equal to one component vector if the other component is zero. 
 ## LEARNING AIDS
	**Common Mistakes**:
		1.[Error 1]: Forgetting to take the square root at the end.
			[How to avoid]: Always double-check your calculations and remember to take the square root for the final result when solving for a magnitude using the Pythagorean theorem.
		2.[Error 2]: Confusing the resultant vector with a component.
			[How to avoid]: Clearly identify which vectors are components and which one is the resultant.
	**Quick Tips**:
		1.[Helpful shortcut]: Recognizing common Pythagorean triples (e.g., 3-4-5, 5-12-13) can sometimes speed up calculations.
		2.[Memory aid]: Draw a diagram to visualize the vector components and their relationship to the resultant vector. This can help avoid errors in calculations.

ABDUL JILANI BASHA · Answer

$30\,{\rm{km}}{{\rm{h}}^{ - 1}}$

ABDUL JILANI BASHA · Answer

The correct Option is "$30\,\sqrt 3 {\rm{\;km}}{{\rm{h}}^{ - 1}}$"

ABDUL JILANI BASHA · Answer

$30\,\sqrt {2{\rm{\;}}} {\rm{km}}{{\rm{h}}^{ - 1}}$

ABDUL JILANI BASHA · Answer

Zero

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