1. Kinematics in Two Dimensions
Chapter 3

2. Displacement, Velocity, and Acceleration
So far, these concepts have been used to describe straight line (or one dimensional) motion.
In reality, these concepts can also describe curved motion.
In such situations, the typical symbol x used for displacement is replaced with the symbol r (most likely for radius!)

3. Definitions Refined
Displacement is the shortest distance between two positions (using vector addition)
Average Velocity follows the same convention as always. Remember…average velocity vector must be in the same direction as the displacement.
Average Acceleration is defined the same as it is for straight line motion. Direction will be the same as the change in velocity

4. Equations of Kinematics In Two Dimensions
X component
Y component

5. What is the Meaning of All This??
Consider the motion of a jet with two engines. The engines are placed perpendicular to each other. One on the x-axis, the other on the y-axis.
The x part of motion occurs exactly as it would if the y part did not occur at all.
The y part occurs exactly as it would if the x part of the motion did not exist.

6. So…. X and y motions are independent of one another.
The “common factor” is most often time!
Consider the jet then watch the demonstration.

7. Projectile Motion
Consider an object being thrown horizontally or up at an angle. What path does the object take?
This path is called the projectile’s trajectory.
Solving projectile motion problems requires knowledge of kinematics equations and acceleration due to gravity.

8. Projectile Motion Equations
It is absolutely necessary to remember that projectile motion involves two simultaneous independent motions.
A horizontal flight
A vertical free fall
Considering what we know about these two types of motion, what is accelerating a projectile?

9. Horizontal Component of Motion
Once the projectile is launched, the horizontal velocity remains constant!!!!
There is no horizontal acceleration.
Useful equations for the horizontal component include:

10. Vertical Component of Motion
Gravity causes vertical acceleration. Therefore, this component of motion can be treated like free fall where a=9.8m/s2
If the projectile if launched horizonally,