Introduction to 2D Projectile Motion

2. Introduction to 2D Projectile Motion

3. Types of ProjectilesWhich one is NOT a projectile?

4. Projectile Motion Basics • PM is an example of 2-dimensional motion. • Something is fired, thrown, or shot, near the earth’s surface, and is in free- fall. • Horizontal velocity is constant. • Vertical velocity is accelerated. • Air resistance is ignored.

5. Projectile Motion Strategies • Resolve vector into components. • Displacement, velocity, and acceleration • Work as two one-dimensional problems. • Each dimension can obey different equations of motion.

6. Horizontal Component of Velocity • Vx is constant • Not accelerated • Not influenced by gravity • Follows equation:

7. Horizontal Component of Velocity Newton's 1st Law

8. Vertical Component of Velocity • Undergoes accelerated motion • Accelerated by gravity (9.8 m/s2 down)

9. Horizontal and Vertical Newton's 2nd Law

10. vo Horizontally Projected

11. Time is the Key! • Determine the time that the object is in flight with kinematics. • The vertical, y, time is the time that you use in the horizontal, x, dimension. • The other parameters may be found by using the various kinematic equations

16. LAB- Shoot For Your Grade

17. …you must first resolve the initial velocity into components. Viy = Vi sin  Vix = Vi cos  At an Angle projectile problems… Vi 

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

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

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

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

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

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

24. 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

25. 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

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

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

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

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

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

31. vo  Notes about Launch Angle • 45o will yield the longest range • A complimentary angle will yield an equal range

32. Time of flight equal to drop time Initial vertical velocity is 0 m/s Horizontal velocity never changes Acceleration is always g Time to apex is ½ total time of flight Initial vertical velocity is vsinq Initial horizontal velocity is vcosq Acceleration is always g Key Facts:Horizontal Vertical