1. Projectile Motion
Section 3.3

2. What is a projectile? Projectile
Object thrown or launched into the air and is subject to gravity.
Parabolic Trajectory

3. Horizontal and Vertical Components
Since a projectile moves in 2-dimensions, it therefore has 2 components just like a resultant vector.

4. Horizontal Velocity Component
NEVER changes - ignore air resistance
Initial horizontal velocity equals the final horizontal velocity
Gravity DOES NOT work horizontally to increase or decrease the velocity.

5. Vertical Velocity Component
Velocity changes (due to gravity) – free fall
Constant acceleration
Use constant acceleration equations with viy = 0 m/s

6. Trajectory
Together, the horizontal and vertical components produce what is called a trajectory or path. This path is parabolic in nature.

7. Projectile Types
Horizontal Free Fall Launched at an Angle

8. Horizontally Launched
Projectiles which have NO upward trajectory and NO initial VERTICAL velocity. Vx = constant Viy = 0 m/s

9. Horizontal Launch Δx = vi Δt + ½ a (Δt )2 Horizontal
Vx = constant Δx = vx Δt
a = 0 m/s2
Vertical
Viy = 0 m/s Δy = ½ g (Δt )2
g = m/s2
* Can use these assumptions for all constant acceleration equations

10. Example 1
A plane traveling with a horizontal velocity of 125 m/s is 525 m above the ground. The pilot decides to drop some supplies to designated target below.
How long are the supplies in the air?
How far away from point where it was launched will the supplies land?

11. Example 2
The Leo Frigo Memorial Bridge is 62 m above the Fox River. Suppose you kick a rock horizontally off the bridge. The rock hits the water 12 m from the edge of the bridge. Find the speed at which you kicked the rock.

12. Free fall assumptions will also apply
Launched at an Angle
Since the projectile was launched at a angle, the velocity MUST be broken into components!!!
Vix = Vi cos θ
Viy = Vi sin θ
Free fall assumptions will also apply

13. Derive equation
Given just the angle and the distance traveled, find an equation for the height of the object.

14. Example
A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees.
(a) How long is the ball in the air?

15. Example
A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees. (b) How far away does it land?

16. Example
A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees.
(c) How high does it travel?