1. Mechanics Lecture 2, Slide 1 Vectors and 2d-Kinematics Continued Comments on Homework Summary of Vectors and 2-d Kinematics Homework Solutions

2. Homework Results Vectors and 2-d kinematics Mechanics Lecture 1, Slide 2 Average=87% No attempt = 14 Awesome Job! See Me or TAs

3. Homework 1 results Mechanics Lecture 1, Slide 3 Average=62.5% Among those who made an attempt Average=74.7%

4. Great Suggestions for Success Mechanics Lecture 1, Slide 4

5. Questions/Suggestions Mechanics Lecture 1, Slide 5 Each component can be treated separately. Remember that they are component of a vector Kinematic equations for displacement,velocity and acceleration are the source for the derived equations. For this situation the horizontal component of the velocity remains constant. The vertical component of velocity changes due to the gravitational acceleration.

6. Mechanics Lecture 2, Slide 6 Vectors and 2d-kinematics – Main Points

7. Mechanics Lecture 2, Slide 7 Vectors and 2d-kinematics – Main Points

8. Vectors and 2d-kinematics Fundamental Equations Mechanics Lecture 2, Slide 8

9. Source of Projectile Trajectory Equations Mechanics Lecture 1, Slide 9 Horizontal Vertical Boring

10. Catch problem responses Mechanics Lecture 1, Slide 10

11. Catch 2 responses Mechanics Lecture 1, Slide 11

12. Soccer Kick responses Mechanics Lecture 1, Slide 12

13. Cannonball Responses Mechanics Lecture 1, Slide 13

14. Ballistic Projectile Motion Quantities Mechanics Lecture 2, Slide 14 Initial velocity  speed,angle Maximum Height of trajectory, h=y max Range of trajectory, D Height of trajectory at arbitrary x,t “Hang Time” Time of Flight, t f

15. Derived Projectile Trajectory Equations Mechanics Lecture 1, Slide 15 Height of trajectory as f(x), y(x) Height of trajectory as f(t), y(t) Range of trajectory Time of Flight (“Hang Time”) Maximum height

16. Homework Solutions-Baseball Mechanics Lecture 1, Slide 16

17. Homework Solutions-Baseball Mechanics Lecture 1, Slide 17

18. Homework Hints- Baseball Stadium Wall Mechanics Lecture 1, Slide 18

19. Homework Hints – Stadium Wall Mechanics Lecture 1, Slide 19 Calculate time to reach wall using v x : Calculate y position at time to reach wall:

20. Homework Solutions-Baseball Stadium Mechanics Lecture 1, Slide 20

21. Homework Hints-Catch Mechanics Lecture 1, Slide 21

22. Homework Hints-Catch Mechanics Lecture 1, Slide 22

23. Homework Hints-Catch Mechanics Lecture 1, Slide 23

24. Homework Solutions-Catch Mechanics Lecture 1, Slide 24

25. Homework Solutions-Catch Mechanics Lecture 1, Slide 25

26. Homework Solutions-Catch Mechanics Lecture 1, Slide 26

27. Homework Hints-Catch 2 Mechanics Lecture 1, Slide 27

28. Homework Hints-Catch 2 Mechanics Lecture 1, Slide 28 v V x is constant ! Kinetic energy should be same as when ball was thrown. Y- component of velocity would be downward.

29. Homework Hints-Catch 2 Mechanics Lecture 1, Slide 29 Same conditions as before

30. Homework Hints – Soccer Kick & Cannonball Mechanics Lecture 1, Slide 30

31. Homework Hints – Soccer Kick & Cannonball Mechanics Lecture 1, Slide 31

32. Homework Hints – Soccer Kick & Cannonball Mechanics Lecture 1, Slide 32

33. Homework Solutions-Catch Mechanics Lecture 1, Slide 33

34. Homework Hints-Catch Mechanics Lecture 1, Slide 34

35. Homework Hints-Catch 2 Mechanics Lecture 1, Slide 35

36. Homework Solutions-Catch 2 Mechanics Lecture 1, Slide 36 v V x is constant ! Kinetic energy should be same as when ball was thrown. Y- component of velocity would be downward.

37. Homework Solutions-Catch 2 Mechanics Lecture 1, Slide 37 Same conditions as before

38. Homework Hints – soccer kick Mechanics Lecture 1, Slide 38

39. Homework Solutions– soccer kick Mechanics Lecture 1, Slide 39

40. Homework Solutions – soccer kick Mechanics Lecture 1, Slide 40

41. Homework Solutions - Cannonball Mechanics Lecture 1, Slide 41

42. Cannonball Solutions Mechanics Lecture 1, Slide 42

43. Cannonball- Solutions Mechanics Lecture 1, Slide 43

44. Mechanics Lecture 2, Slide 44 Vectors and 2d-kinematics – Main Points

45. Mechanics Lecture 2, Slide 45 Time spend in the air depends on the maximum height Maximum height depends on the initial vertical velocity v train car

46. Trigonometric Identity for range equation Mechanics Lecture 2, Slide 46 http://mathworld.wolfram.com/Cosine.html http://mathworld.wolfram.com/Sine.html

47. Trigonometric Identities relating sum and products Mechanics Lecture 2, Slide 47 List of trigonometric identities

48. Hyperphysics-Trajectories Mechanics Lecture 1, Slide 48 http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html