# Chapter 5: Motion in Two Dimensions

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

To create this photograph, a camera shutter was opened eighteen times, producing eighteen consecutive images of the snowboarder as he jumped. You can clearly see that there are both vertical and horizontal components to his overall parabolic 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 shutter openings, knowing only the maximum vertical height attained by the snowboarder. You will also know how to accurately estimate his maximum vertical height using only the time he spent in the air.

- 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—including springs, pendulums, rotating disks, and orbiting satellites—can be understood using the simple harmonic motion equations.

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