The Question is from neet-chemistry motion-in-a-plane additionsubtraction-and-resolution-of-vectors, and it was created by the author A.RAMA NAGESWARARAO

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

A.RAMA NAGESWARARAO · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
**Primary Concept**: Vector Resolution into Rectangular Components
**Related Topics**: Velocity, Pythagorean Theorem, Vector Addition
**Prerequisites**: Understanding of vectors, components of vectors, and the Pythagorean theorem.
## SOLUTION PATHWAY
**Given Information**:
Total velocity (v) = 60 km/h
One component of velocity (v1) = 30 km/h
Let the other component be v2.
**Method & Steps**:
1.  **Understanding Vector Components:** The total velocity is the resultant of two rectangular components. We can visualize this using a right-angled triangle where the total velocity is the hypotenuse, and the components are the sides.
Reasoning: Vector components are perpendicular to each other.
Formula/Rule: The Pythagorean Theorem:  $v^2 = v_1^2 + v_2^2$
2.  **Applying the Pythagorean Theorem:** 
Working: We can find the other component by rearranging the Pythagorean equation:  $v_2^2 = v^2 - v_1^2$
$v_2^2 = (60)^2 - (30)^2$
$v_2^2 = 3600 - 900$
$v_2^2 = 2700$
Key Point: Solve for the unknown component after substituting all known values.
3.  **Final Calculation:**
Working: $v_2 = \sqrt{2700} = \sqrt{900 * 3} = 30\sqrt{3}$
Result:  $v_2 = 30\sqrt{3} km/h$
Verification:  Substituting the values back into the original equation: $(60)^2 = (30)^2 + (30\sqrt{3})^2$ which simplifies to $3600 = 900 + 2700 = 3600$, verifying our answer.
## OPTION ANALYSIS
[A] :x: This answer does not use the Pythagorean theorem, and is therefore incorrect.
[B] ✓: This is the correct component calculated using the Pythagorean theorem.
[C] :x: The value under the root is incorrect. This option is therefore incorrect
[D] :x:  If one component is 30, the other component cannot be zero, as the resultant is 60. This is incorrect.
## LEARNING AIDS
**Common Mistakes**:
1. **Incorrect application of Pythagoras theorem:** Forgetting to square the values or incorrectly rearranging the equation. Always ensure the hypotenuse is the total velocity.
2. **Confusion with vector addition:** Not recognizing that components add up vectorially using the Pythagorean theorem.
**Quick Tips**:
1. **Visualizing with a triangle:** Draw a right triangle with the total velocity as the hypotenuse. This helps in correctly applying the Pythagorean theorem.
2. **Remembering Pythagorean Triples:** Recognize some common Pythagorean triples (like 3,4,5) or multiples to speed up calculations.

A.RAMA NAGESWARARAO · Answer

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

A.RAMA NAGESWARARAO · Answer

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

A.RAMA NAGESWARARAO · Answer

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

A.RAMA NAGESWARARAO · Answer

Zero

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