1. Two-dimensional Motion and Vectors Projectile Motion
Chapter 3: Section 3

2. Learning Targets Recognize examples of projectile motion
Describe the path of a projectile as a parabola
Resolve vectors into their components and apply the kinematic equations to solve problems involving projectile motion
P2.2g, P3.4e,

3. Two-Dimensional Motion
When an object is propelled into the air in a direction other than straight up or down, the velocity, acceleration and displacement of the object do not all point in the same direction
To solve problems involving projectiles , the motion of the object must be broken down into its x and y components

4. Components simplify projectile motion
When a long jumper approaches his jump, he runs along a straight line, the x-axis.
When he jumps, his velocity has both horizontal and vertical components

5. What are Projectiles?
Objects that are thrown or launched into the air and are subject only to the force of gravity are called projectiles
A projectile is any object that once projected or dropped continues in motion by its own inertia and is influenced only by the downward force of gravity.
Examples include softballs, footballs, and arrows

6. What about an Upward force?
A force is not required to keep an object in motion.
A force is only required to maintain an acceleration.
In the case of a projectile that is moving upward, there is a downward force and a downward acceleration.
As the object moves upward it slows down.
As the object moves downward it speeds up.

7. Projectiles follow parabolic trajectories
The path of a projectile is a curve called a parabola

8. Horizontal Motion of Projectiles
If an object has an initial horizontal velocity, there will be horizontal motion throughout the flight of the projectile
This horizontal velocity can be considered constant if there is no air resistance
With air resistance, a projectile slows down as it collides with air particles

9. Vertical Motion of Projectiles
Projectile motion is simply free fall with an initial horizontal velocity
If the projectile rises towards a peak, it’s free fall acceleration slows down (19.6 m/s to 9.8 m/s to 0 m/s)
As a projectile falls, it speeds up (0 m/s to m/s to m/s to ...).

10. Note that the horizontal velocity is constant

11. The most important concepts about projectile motion are that horizontal velocity remains constant during the course of the trajectory and vertical velocity changes by 9.8 m/s every second (free fall acceleration)

12. Why do these balls fall at the same rate? Even though the red
ball has no initial
horizontal velocity, both
balls have identical
vertical velocity and are
subject to free fall
acceleration

13. Review of Projectile Motion
Projectiles are objects that when thrown or launched into the air are subject only to the force of gravity
The horizontal motion of a projectile will remain constant
A force is not required to keep an object in motion; only to cause and acceleration
The vertical motion of a projectile is influenced by free fall acceleration
a = m/s2

14. Projectile Motion Equations
Vertical Motion of a Projectile that Falls From Rest
vy,f = ay∆t
vy,f2 = 2ay∆y
∆y = ½ ay(∆t)2

15. Projectile Motion Equations
Horizontal Motion of a Projectile
∆x = vx∆t

16. Sample Problems
The Royal Gorge Bridge in Colorado rises 321 m above the Arkansas River. Suppose you kick a rock horizontally off the bridge. The magnitude of the rock’s horizontal displacement is 45.0 m. Find the speed at which the rock was kicked
A baseball rolls off a 0.70 m high desk and strikes the floor 0.25 m away from the base of the desk. How fast was the ball rolling?

17. Animation: Projectile Motion
T- 1.0/simulations/simsa79a.html?sim=Projectil e_Motion
Look at effect of air resistance, mass (with and without air resistance), angle