Some of the content of this guide was modeled after a guide published by OpenStax and has been adapted for the NWP Learning Commons in January 2022. This work is licensed under a Creative Commons BY 4.0 International License.
Bringing in the unit vectors, i and j, that were reviewed in the fundamentals section, linear motion can be expressed in two or three dimensions with the same logic. The velocity vector in the example below can be described as its velocity in the x-direction and its velocity in the y-direction. To find the resultant velocity, simply treat x and y as the sides of a right-angle triangle and use Pythagorean Theorem to calculate the resultant magnitude. From there, use a trigonometric ratio to calculate the angle with respect to the x-axis.
The same idea can be applied to the resultant vector to calculate the x and y components:
This can further be generalized, as the resultant vector is composed of its magnitude multiplied by cosine of the angle in the x-direction plus sine of the angle in the y-direction:
