MT4: Vector A has a magnitude of 2.5 m/s at a direction of 18° and vector B has a magnitude of 4.5 m/s at a direction of 240°. • Sketch the two vectors roughly to scale, and find their sum C = A + B using a graphical method. • Find the components of A and B, including any necessary negative signs Find the magnitude and direction of using the algebraic/components method

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**MT4: Vector Analysis Exercise**

- **Problem Statement**: 
  - Vector \(\vec{A}\) has a magnitude of 2.5 m/s at a direction of 18°.
  - Vector \(\vec{B}\) has a magnitude of 4.5 m/s at a direction of 240°.

- **Tasks**:
  1. **Graphical Representation**:
     - Sketch the two vectors roughly to scale.
     - Find their sum \(\vec{C} = \vec{A} + \vec{B}\) using a graphical method.

  2. **Component Analysis**:
     - Determine the components of \(\vec{A}\) and \(\vec{B}\), including any necessary negative signs.

  3. **Magnitude and Direction Calculation**:
     - Find the magnitude and direction of \(\vec{C}\) using the algebraic/components method.

**Instructions**:

- Ensure sketches are clear and vectors are drawn accurately with proper angles and lengths.
- Use trigonometric functions to calculate vector components.
- Apply appropriate mathematical formulas to determine the resultant vector's magnitude and direction.
- Review vector addition and resolution techniques in kinematic contexts.

---
This exercise will enhance your understanding of vector operations and their applications in physics.
Transcribed Image Text:**MT4: Vector Analysis Exercise** - **Problem Statement**: - Vector \(\vec{A}\) has a magnitude of 2.5 m/s at a direction of 18°. - Vector \(\vec{B}\) has a magnitude of 4.5 m/s at a direction of 240°. - **Tasks**: 1. **Graphical Representation**: - Sketch the two vectors roughly to scale. - Find their sum \(\vec{C} = \vec{A} + \vec{B}\) using a graphical method. 2. **Component Analysis**: - Determine the components of \(\vec{A}\) and \(\vec{B}\), including any necessary negative signs. 3. **Magnitude and Direction Calculation**: - Find the magnitude and direction of \(\vec{C}\) using the algebraic/components method. **Instructions**: - Ensure sketches are clear and vectors are drawn accurately with proper angles and lengths. - Use trigonometric functions to calculate vector components. - Apply appropriate mathematical formulas to determine the resultant vector's magnitude and direction. - Review vector addition and resolution techniques in kinematic contexts. --- This exercise will enhance your understanding of vector operations and their applications in physics.
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