1. 2.2 Motion in 2-D: The Component Method
In Section 2.1 we used the Scale Diagram Approach to solve vector addition in two-dimensions. Scale Diagrams may not be precise and can be awkward to add without a map and an appropriate scale.
An algebraic approach is more efficient and accurate. 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 trig ratio to use, as well as which directional sign to include for each component.

2. 2.2 The Component Method
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.

3. 2.2 Motion in 2-D: Component Method
Once all individual x- & y- components are found, combine them respectively to find the resultant x- & y-components.
The magnitude of the resultant vector is found using the Pythagorean Theorem of the resultant x- & y-components.
The direction of the resultant vector is found using an inverse tangent function (θ= tan −1 ) of the resultant x- & y-components.
In order to help visualize the resultant vector direction, include a thumbnail sketch of the combined resultant x- & y-components.

4. 2.2 The Component Method
A Flow Chart Summary of The Component Method. SP # 1,2 p

5. 2.2 Homework Practice # 1 p.69 Practice # 1,2 p.71
Questions #1,3,5,7 p.75