Component Method of Vector Addition
Component Method of Vector AdditionBy: Aemie joy M. Odsinada IV-DarwinThe component method of addition can be summarized this way:
Using trigonometry, find the x-component and the y-component for each vector. Refer to a diagram of each vector to correctly reason the sign, (+ or -), for each component.
Add up both x-components, (one from each vector), to get the x-component of the total.
Add up both y-components, (one from each vector), to get the y-component of the total.
Add the x-component of the total to the y-component of the total, and then use the Pythagorean theorem and trigonometry to get the size and direction of the total.
Right triangle trigonometry is used to find the separate components.
Let's take this all one step at a time. First, let's visualize the x-component and the y-component ofd1. Here is that diagram showing thex-componentinredand they-componentingreen:
The two components along with the original vector form aright triangle. Therefore, we can useright triangle trigonometryto find the lengths of the two components. That is, we can use the'SOH-CAH-TOA'type of definitions for the sine, cosine, and tangent trigonometry functions.
Finding the first x-component.
Let's find the x-component ofd1. Notice that the x-component is adjacent to the angle of 34 degrees, so, we will use the cosine function since it relates an acute angle, the adjacent side to that angle, and the hypotenuse of a right triangle:
Now, using trigonometry like this willnottell us the sign, (+ or -), of this component, (or any other). So, we must check the diagram for positive or negative directions. This x-component is aimed to the right, so, it is positive:
(Again, remember that these calculations presented here have decimals that have been truncated. Presenting calculations to many more decimals does not help clarify methods, and, also, it violates several rules of significant digits. In other words, these calculations are approximate. The calculator below keeps many more decimal places, so, its outputs will differ slightly.)
Again, check the diagram for positive or negative directions. The y-component aims up, so, it is positive:Finding the first y-component.Now, let's find the y-component ofd1. Notice that the y-component is opposite to the angle of 34 degrees, so, we will use the sine function since it relates an acute angle, the opposite side to that angle, and the hypotenuse of a right triangle:
The calculated values for the first set of components
Here is the diagram now showing the values for the x-component and y-component ofd1:
Find the resultant vector of A and B given in the graph below. (sin30=1/2, sin60=3/2, sin53=4/5, cos53=3/5)
We use trigonometric equations first and find the components of the vectors then, make addition and subtraction between the vectors sharing same direction.
