# Chapter 5: Motion in Two Dimensions

**At Grade**Created by: CK-12

**Credit**: Davide Costanzo (Flickr: BadSwan)

**Source**: http://www.flickr.com/photos/badswan/8203513475/

**License**: CC BY-NC 3.0

In this photograph, the camera shutter was opened eighteen times, producing eighteen consecutive images of a snowboarder as he jumped. Clearly, there were horizontal and vertical aspects to his motion. To complete calculations on this sort of two-dimensional motion, it is necessary to consider the vertical and horizontal **vectors** separately. By the end of this chapter, you will be able to accurately estimate the time elapsed over the course of this image and between photos knowing only the maximum vertical height the snowboarder attained. You will also know how to accurately estimate the maximum vertical height using only the time he spent in the air.

## Chapter Outline

- 5.1. Projectile Motion for an Object Launched Horizontally
- 5.2. Projectile Motion for an Object Launched at an Angle
- 5.3. Circular Motion
- 5.4. Centripetal Force
- 5.5. Simple Harmonic Motion

### Chapter Summary

Using kinematic equations and the understanding that vertical acceleration does not affect horizontal velocity, it is easy to calculate the height from which an object is launched or the location at which it will land. These equations can also be used to understand how satellites maintain a consistent orbit; circular motion and centripetal acceleration equations can also serve this purpose. Perhaps most interestingly, everything that undergoes periodic motion (springs, pendulums, rotating disks, orbiting satellites) can be understood using the simple harmonic motion equations.

### Image Attributions

**[1]****^**Credit: Davide Costanzo (Flickr: BadSwan); Source: http://www.flickr.com/photos/badswan/8203513475/; License: CC BY-NC 3.0