Kinematics The Component Method

Recall Vectors are quantities that have both magnitude and direction. Graphically, their sum is calculated by adding the vectors “tip-to-tail”. Graphical method is efficient for co-linear vectors and vectors problems with two vectors only. What if there are more? The component method!

The Component Method Method that resolves each vector into its x- components and y-components. The resultant is calculated through the addition of these components.

Example #1 Determine the resultant of the following vectors using the component method:

Solution a: b: Vector X-component Y-component 3.93m 3.27m 10m 250 ax ay 15m 300 b: bx by 3.27m 3.93m

Example #2 Determine the resultant of the following vectors using the component method:

Solution a: b: c: Vector X-component Y-component ax ay 10km 300 bx 300 by 30km 450 c: cy cx

1.11km 19.87 km