Lesson 2.2 ~ Motion in 2-D: The Component Method

• In order to add vectors in two-dimensions algebraically, we will use the Component Method.
• To start off, draw thumbnail sketches of each individual 2-D vector being broken into its respective components. This helps to visualize which trigonometric ratio to use, as well as which directional sign to include for each component.
• All 2-D vectors can be broken into their respective horizontal (x) and vertical (y) components. This is done using sinθ and cosθ trig ratios.
• 2.2 Motion in 2-D: Component Method

  1. draw a sketch
  2. Once all the individual x & y components are found, combine them respectively to find the resultant x & y components.
  3. The magnitude of the resultant vector is found using Pythagorean Theorem of the resultant x & y components

  [a² + b² = c²]

  
  

  4. The direction of the resultant vector is found using an inverse tangent function [θ = tan-1 ] of the resultant x & y components.