1. Two-Dimensional Motion
Chapter 3
Two-Dimensional Motion

2. Projectile Motion
An object may move in both the x and y directions simultaneously
It moves in two dimensions
The form of two dimensional motion we will deal with is called projectile motion

3. Assumptions of Projectile Motion
We may ignore air friction
We may ignore the rotation of the earth
With these assumptions, an object in projectile motion will follow a parabolic path

4. Rules of Projectile Motion
The x- and y-directions of motion are completely independent of each other
The x-direction is uniform motion
ax = 0
The y-direction is free fall
ay = -g

5. Some Details About Horizontal Projectiles
x-direction
ax = 0
vxo = vx = constant
x = vxot
This is the only operative equation in the x-direction since there is uniform velocity in that direction

6. More Details About Horizontal Projectiles
y-direction
vyo = 0
free fall problem
a = -g
take the positive direction as upward
uniformly accelerated motion, so the motion (kinematic) equations all hold

7. Example 1
A plane traveling at an altitude of m drops supplies to polar explorers 270 m directly ahead of it. If the supplies land at the explorers’ feet, how fast was the plane traveling?

8. Example 2
A polar bear rolls a bowling ball with a speed of 2.0 m/s off a 10.0 m high diving board. How far away should another polar bear be treading water in order to catch the bowling ball?