1. Projectile Motion

2. If you throw a javelin… What affects it’s flight? Gravity
How hard you throw it (initial velocity)
What angle you throw it at
Air resistance (shape of javelin)
Mass
Which one of these has no affect?

3. Let’s take a look at how they affect flight!

4. We call the arc of the javelin toss:
Projectile Motion
Projectiles travel along a curved trajectory

6. Projectile Motion
A video introduction

7. What is a Projectile? Projectile
– an object that moves along a 2-D curved trajectory
- does not have any propulsion when in flight
Examples:
Football, baseball, tennis ball, etc
Bullets
Snow boarders in a half pipe
Cliff divers

8. Projectile Motion Example # 1

9. What do you notice about these two projectiles?

10. Did you notice?
The projectiles hit the ground at the same time regardless of horizontal velocity
Object accelerates downwards (at 9.81 m/s2 – acceleration due to gravity)
Horizontal displacement stays constant throughout motion

11. Conclusions about Projectile motion
The horizontal component of a projectile’s velocity is constant (no acceleration)
Projectile experiences constant downwards acceleration (gravity)
Horizontal and vertical motion of a projectile are independent of each other (except they have a common time)

13. Projectile Motion Example # 2

14. Important Variables Time – Δt Velocity – v Height – Δdy Distance – ΔdX
Acceleration – a
Launch Angle - θ

15. Strategy to Solving Projectile Motion Problems
Analyze horizontal motion and vertical motion independently
Separate the velocity vector into x- and y- components
Remember: Time is common between them

16. Horizontal motion:
- Constant velocity (0 accel.) in the x direction
- Equation : v = d/t
Vertical motion:
- Constant acceleration m/s2 [down]
- Use the accel. equations we used previously

17. Two Types of Problems: One Dimensional Problems (no horiz
Two Types of Problems: One Dimensional Problems (no horiz. Velocity) Case 1: Object dropped from rest Case 2: Object thrown directly upwards Two Dimensional Problems: Case 3: Rolled over an edge Case 4: Shot at an angle Let’s analyze the four cases!

18. For Two Dimensional Problems:
Break the initial velocity into horizontal and vertical components (using the given angle and trigonometry) vy θ vx

20. Projectile Motion Example # 3

21. Example Question (Case 3) A tennis ball is rolled off a counter at 8 m/s, what will it’s position be after 3s? Example Question (Case 4) A golfer strikes a golf ball on level ground. The ball leaves the ground with an initial velocity of 42 m/s [32o above the horizontal]. a) What will the ball’s position be after 4 s? b) What will be the maximum height attained?