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# Chapter 3: Two-Dimensional and Projectile Motion

Difficulty Level: At Grade Created by: CK-12

## Introduction

### The Big Idea

In this chapter, we explore the motion of projectiles under the influence of gravity --- fired cannonballs, thrown basketballs, and other objects that have no way of propelling themselves and do not experience significant air resistance. We know that vectors can be separated into components (see first lesson); if they are separated into perpendicular components the motion along each component can be treated independently.

This is the insight that allows us to solve two dimensional projectile motion problems: we break any initial velocity vector into a component parallel to the ground and a component perpendicular to it. The force of gravity --- which will be explained in more detail later --- accelerates any object near the surface of the earth toward its center at a rate of g=9.8m/s2\begin{align*} g = 9.8 \mathrm{m/s^2} \end{align*}. This acceleration is in the direction perpendicular to the surface of the earth, conventionally labeled y\begin{align*} y \end{align*}.

Since in projectile motion under the sole influence of gravity any acceleration the object experiences is in the y\begin{align*} y \end{align*} direction, its horizontal, or x\begin{align*} x \end{align*}, velocity remains constant throughout its flight (at least in the absence of air resistance, which we ignore for the time being). To solve two dimensional motion problems, we apply the kinematics equations of one-dimensional motion to each of the two directions. In the y\begin{align*} y \end{align*} direction, we can use the uniform acceleration equations to solve for time in flight. Using this time, we can find how far the object traveled in the x\begin{align*} x \end{align*} direction also.

Chapter Outline

## Summary

Breaking vectors into components, relative velocity and projectile motion are all covered in this chapter.

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