Understanding 2D Projectile Motion: Trajectories and Components

1. Introduction to 2D Projectile Motion

2. Projectile Motion • An example of 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. y x Trajectory of Projectile This projectile is launched an an angle and rises to a peak before falling back down.

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

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

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

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

8. y y x x t t Position graphs for 2-D projectiles

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

10. y x Trajectory of Projectile Velocity is tangent to the path for the entire trajectory. v v v vo vf

11. y x Trajectory of Projectile The velocity can be resolved into components all along its path. vx vx vy vy vx vy vx vy vx

12. y x Trajectory of Projectile Notice how the vertical velocity changes while the horizontal velocity remains constant. vx vx vy vy vx vy vx vy vx

13. y x Trajectory of Projectile Where is there no vertical velocity? vx vx vy vy vx vy vx vy vx

14. y x Trajectory of Projectile Where is the total velocity maximum? vx vx vy vy vx vy vx vy vx

15. 2D Motion • Resolve vector into components. • Position, velocity or acceleration • Work as two one-dimensional problems. • Each dimension can obey different equations of motion.

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

17. Horizontal Component of Velocity

18. 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)

19. Horizontal and Vertical

20. Horizontal and Vertical

21. vo Launch angle Zero launch angle

22. vo  Launch angle Positive launch angle

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

24. t to = 0 Symmetry in Projectile Motion Time of flight

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