Freshman Physics 1#4 Vectors Resolution Ethiopian University

Introduction

This tutorial provides a comprehensive guide to understanding vector resolution as presented in the Freshman Physics video from Ethiopian University. Mastering vector resolution is crucial for solving problems in physics and engineering, as it allows you to break down complex vectors into their component parts.

Step 1: Understanding Vectors

• A vector is a physical quantity that has both magnitude and direction.
• Common examples include force, velocity, and displacement.
• Vectors can be represented graphically with arrows, where the length indicates magnitude and the direction indicates orientation.

Step 2: Components of Vectors

• Any vector can be broken down into two perpendicular components: horizontal (x-axis) and vertical (y-axis).
• To visualize this, draw a right triangle where:
  • The hypotenuse represents the vector.
  • The base represents the horizontal component.
  • The height represents the vertical component.

Step 3: Resolving Vectors into Components

• To resolve a vector into its components, follow these steps:
  1. Identify the angle θ that the vector makes with the horizontal axis.
  2. Use trigonometric functions to find the components:
     • Horizontal Component (Vx): [ Vx = V \cdot \cos(θ) ]
     • Vertical Component (Vy): [ Vy = V \cdot \sin(θ) ]
  • Here, V is the magnitude of the vector.

Step 4: Practical Example

• Consider a vector with a magnitude of 10 units at an angle of 30 degrees.
  1. Calculate the horizontal component: [ Vx = 10 \cdot \cos(30°) \approx 8.66 \text{ units} ]
  2. Calculate the vertical component: [ Vy = 10 \cdot \sin(30°) = 5 \text{ units} ]

Step 5: Vector Addition

• When adding vectors, the components can be added separately:
  1. For two vectors A and B:
     • Resolve both into their components.
     • Add the horizontal components together: [ R_x = A_x + B_x ]
     • Add the vertical components together: [ R_y = A_y + B_y ]
  2. The resultant vector R can then be found using: [ R = \sqrt{R_x^2 + R_y^2} ]
  3. The angle of the resultant vector can be found using: [ θ_R = \tan^{-1}\left(\frac{R_y}{R_x}\right) ]

Conclusion

Understanding vector resolution is essential for tackling physics problems effectively. By breaking vectors into components and using trigonometric functions, you can simplify complex scenarios into manageable calculations. Practice resolving various vectors and adding them to reinforce your understanding. For further learning, explore more advanced topics in vector analysis or apply these concepts to real-world physics problems.