1. Introduction to 2D Projectile Motion
Which pictures are examples of projectile motion?

2. Projectile Motion Must include 2-dimensional motion.
Something is fired, thrown, shot, or hurled near the earth’s surface.
Horizontal velocity is constant.
Vertical velocity is accelerated.
Air resistance is ignored.

3. Trajectory of Projectilex y
This projectile is launched at an angle and rises to a peak before falling back down.

4. Trajectory of Projectilex y
The trajectory of such a projectile is defined by a parabola.

5. Trajectory of Projectilex y
Range
The RANGE of the projectile is how far it travels horizontally.

6. Trajectory of Projectilex y
Maximum
Height
Range
The MAXIMUM HEIGHT of the projectile occurs halfway through its range.

7. Trajectory of Projectilex y g g g g g
Acceleration points down at 9.8 m/s2 for the entire trajectory.

8. To work projectile problems…
…you must first resolve the initial velocity into components.
Vo,y = Vo sin  Vo 
Vo,x = Vo cos 

9. Trajectory of Projectilex y v v v vo vf
Velocity is tangent to the path for the entire trajectory.

10. Trajectory of Projectilex y vx vy vx vy vx vy vx vx vy
The velocity can be resolved into components all along its path.

11. Trajectory of Projectilex y vx vy vx vy vx vy vx vx vy
Notice how the vertical velocity changes while the horizontal velocity remains constant.

12. Trajectory of Projectilex y vx vy vx vy vx vy vx vx vy
Where is there no vertical velocity?

13. Trajectory of Projectilex y vx vy vx vy vx vy vx vx vy
Where is the total velocity maximum?

14. 2D Motion Resolve vector into components.
Position, velocity or acceleration
Work as two one-dimensional problems.
Each dimension can obey different equations of motion.

15. Horizontal Component of Velocity
Newton's 1st Law
Is constant
Not accelerated
Not influence by gravity
Follows equation:
x = Vo,xt

16. Vertical Component of Velocity
Newton's 2nd Law
Undergoes accelerated motion
Accelerated by gravity (9.8 m/s2 down)
Vy = Vo,y - gt
y = yo + Vo,yt - 1/2gt2
Vy2 = Vo,y2 - 2g(y – yo)

17. Symmetry in Projectile Motion vo - vo
Negligible air resistance
Projectile fired over level ground
Launch and Landing Velocity

18. Symmetry in Projectile Motion
to = 0
Time of flight

19. Symmetry in Projectile Motion
to = 0 2t
Projectile fired over level ground
Time of flight
Negligible air resistance

20. Projectile Problem Solving
Break any none X or Y velocity vectors into their X & Y components
Solve for missing variables in either X or Y
DO NOT MIX X & Y INFORMATION IN THE FORMULAS !!!!
Use information found in one plane to solve for information in the other