2. Projectile Motion vovo Launch a projectile horizontally from the top of a cliff. Draw the subsequent path of the projectile marking the position of the projectile at equal intervals of time.

3. Projectile Motion How much time has passed between subsequent positions? 1 unit of time

4. Projectile Motion How much time has passed between subsequent positions? 1 unit of time

5. Projectile Motion How much time has passed between subsequent positions? 1 unit of time

6. Projectile Motion Draw a pair of horizontal and vertical line from each position. Draw an outline of the projectile at each pair of intersecting lines Draw a horizontal and vertical line extending away from the the projectiles initial position.

7. 1 unit Describe the horizontal displacements. Projectile Motion How much time passed between subsequent positions? 1 unit of time Whats the displacement between subsequent positions? Horizontal Displacements are EQUAL

8. 1 unit 5 units 3 units Projectile Motion Describe the vertical displacements. How much time passed between subsequent positions? 1 unit of time Whats the displacement between subsequent positions? xs = Consecutive ODD #s

9. Projectile Motion What does each vertical side of a colored region represent? Left Side x Displacement 1 3 5 Consecutive ODD Numbers

10. Projectile Motion What does each vertical side of a colored region represent? Right Side Distance Fallen 1 4 9 Square of Consecutive Numbers

11. Projectile Motion Whats the relationship between interval displacement and distance fallen? 11 4 3 9 5 Equal 1 +3 4 1 3 +5 9 Distance Fallen = ( x )

12. Projectile Motion Describe the motion of the projectile at subsequent positions. Discuss: Velocity and Acceleration

13. Projectile Motion Describe the motion of the projectile at subsequent positions. CONSTANT Horizontal Velocity

14. Projectile Motion Describe the motion of the projectile at subsequent positions. CHANGING Vertical Velocity

15. Projectile Motion Draw an arrow representing the horizontal velocity at each position. vxvx vxvx vxvx vxvx

16. Projectile Motion Draw an arrow representing the vertical velocity at each position. vxvx vxvx vxvx vxvx vyvy vyvy vyvy vy=0vy=0

17. Projectile Motion Draw an arrow representing the speed at each position. vxvx vxvx vxvx vxvx vyvy vyvy vyvy

18. Projectile Motion Use your knowledge of right triangles to draw in the speed. 90

19. Projectile Motion Draw an arrow representing the speed at each position. vxvx vxvx vxvx vyvy vyvy vyvy v v v v

20. Projectile Motion Use your knowledge of the Pythagorean theorem calculate the speed. 90 v vyvy vxvx v2=vx2+vy2v2=vx2+vy2

21. Projectile Motion Draw an arrow representing the acceleration at each position. vxvx vxvx vxvx v=vxv=vx vyvy vyvy vyvy v v v agag agag agag agag But guess what…

22. Projectile Motion vxvx vxvx vxvx v=vxv=vx vyvy vyvy vyvy agag agag agag v v v agag

23. Kinematics Equations You can still use all these…but just be sure to keep you keep the x and y dimensions separated!

24. Projectile Motion You gotta Keep em separated…. Horizontal MotionVertical Motion The X-stuffThe Y stuff

25. In a Nut Shell There are TWO IMPORTANT RESULTS: in FREE FALL motion: 1. The distance fallen during EACH INTERVAL increases as the RATIO of ODD INTEGERS. 2. The TOTAL DISTANCE fallen during the entire time interval increases as the ratio of SQUARES

26. Projectile Motion Since VELOCITY is relative to the FRAME of REFERENCE, All projectile motion is FREE FALL in the appropriate reference frame. Therefore: The vertical displacements always exhibit: the ratio of squares and ratio of odd integers behavior.