2. Mechanics Lecture 2, Slide 1 Classical Mechanics Lecture 2 Today's Concepts: a) Vectors b) Projectile motion c) Reference frames Reminder Lectures are posted online @ http://www.physics.utah.edu/~springer/phys1500/lectures.html Link to lectures on canvas pages as well…

3. Participation Mechanics Lecture 2, Slide 2

4. Mechanics Lecture 2, Slide 3 Vectors and 2d-kinematics – Main Points

5. Mechanics Lecture 2, Slide 4 Vectors and 2d-kinematics – Main Points

6. Vectors and 2d-kinematics Important Equations Mechanics Lecture 2, Slide 5

7. Mechanics Lecture 2, Slide 6  Think of a vector as an arrow. (An object having both magnitude and direction) The object is the same no matter how we chose to describe it Vectors

8. Mechanics Lecture 2, Slide 7 Think of a vector as an arrow. (An object having both magnitude and direction) The object is the same no matter how we chose to describe it AxAx AyAy VectorsCartesian Polar

9. Mechanics Lecture 2, Slide 8 Vectors

10. Mechanics Lecture 2, Slide 9 The object is the same no matter how we chose to describe it Vectors

11. Mechanics Lecture 2, Slide 10 Vector Addition Add Components!!! Add  Tail to Head

12. Enter Question Text A. B. C. D. E. Mechanics Lecture 2, Slide 11 Vectors and are shown to the right. Which of the following best describes + A B C D E

13. Enter Question Text A. B. C. D. E. Mechanics Lecture 2, Slide 12 Vectors and are shown to the right. Which of the following best describes  A B C D E

14. Mechanics Lecture 2, Slide 13 A B C D E Vectors and are shown to the right. Which of the following best describes + Clicker Question

15. Acceleration Vector Mechanics Lecture 2, Slide 14

16. Acceleration Vector Mechanics Lecture 2, Slide 15

17. Mechanics Lecture 2, Slide 16 A vector can be defined in 2 or 3 (or even more) dimensions: Vectors in 3D

18. Mechanics Lecture 2, Slide 17 Kinematics in 3D

19. Mechanics Lecture 2, Slide 18 Checkpoint 1

20. Mechanics Lecture 2, Slide 19 Horizontal Vertical Boring Projectile Motion

21. Mechanics Lecture 2, Slide 20 A flatbed railroad car is moving along a track at constant velocity. A passenger at the center of the car throws a ball straight up. Neglecting air resistance, where will the ball land? A) Forward of the center of the car B) At the center of the car C) Backward of the center of the car correct Ball and car start with same x position and x velocity, Since a = 0 they always have same x position. Train Demo Clicker Question v train car

22. Moving Rail Car A. B. C. Mechanics Lecture 2, Slide 21 A flatbed railroad car is moving along a track at constant velocity. A passenger at the center of the car throws a ball straight up. Neglecting air resistance, where will the ball land? A) Forward of the center of the car B) At the center of the car C) Backward of the center of the car correct Ball and car start with same x position and x velocity, Since a = 0 they always have same x position. v train car

23. Mechanics Lecture 2, Slide 22 Time spend in the air depends on the maximum height Maximum height depends on the initial vertical velocity v train car

24. Monkey troubles A. B. C. Mechanics Lecture 2, Slide 23 You are a vet trying to shoot a tranquilizer dart into a monkey hanging from a branch in a distant tree. You know that the monkey is very nervous, and will let go of the branch and start to fall as soon as your gun goes off. In order to hit the monkey with the dart, where should you point the gun before shooting? A) Right at the monkey B) Below the monkey C) Above the monkey

25. Mechanics Lecture 2, Slide 24 Monkey x  x o Dart x  v o t Shooting the Monkey…

26. Mechanics Lecture 2, Slide 25 Shooting the Monkey… y = v oy t  1 / 2 g t 2 Still works even if you shoot upwards! y = y o  1 / 2 g t 2 Dart hits the monkey

27. Mechanics Lecture 2, Slide 26 Projectile Motion & Frames of Reference

28. Mechanics Lecture 2, Slide 27 Checkpoint 2 A) Enemy 1 B) Enemy 2 C) They are both hit at the same time 60% of you had incorrect answer… Let’s try again. Enemy 1Destroyer Enemy 2

29. Enemy 1Destroyer Enemy 2 Checkpoint 2 A. B. C. Mechanics Lecture 2, Slide 28 …Which enemy ship gets hit first? A) Enemy 1 B) Enemy 2 C) Same B) The height of the shell fired at ship 2 is less, so ship 2 gets hit first.

30. Mechanics Lecture 2, Slide 29 Enemy 1Destroyer Checkpoint 3 A destroyer fires two shells with different initial speeds at two different enemy ships. The shells follow the trajectories shown. Which enemy ship gets hit first? Enemy 2 A) Enemy 1 B) Enemy 2 C) They are both hit at the same time 66% of you had incorrect answer… Let’s try again.

31. Checkpoint 3 A. B. C. Mechanics Lecture 2, Slide 30 Enemy 1DestroyerEnemy 2 …Which enemy ship gets hit first? A) Enemy 1 B) Enemy 2 C) Same C) they both achieve the same height so they remain in the air the same amount of time

32. Range Mechanics Lecture 2, Slide 31

33. Range Mechanics Lecture 2, Slide 32 MAXIMUM range OCCURS AT 45 0

34. Trigonometric Identity for range equation Mechanics Lecture 2, Slide 33 http://mathworld.wolfram.com/Cosine.html http://mathworld.wolfram.com/Sine.html

35. Trigonometric Identities relating sum and products Mechanics Lecture 2, Slide 34 List of trigonometric identities

36. Question 2 Mechanics Lecture 2, Slide 35

37. Question 2 Mechanics Lecture 2, Slide 36

38. Mechanics Lecture 2, Slide 37 Field Goal Example A field goal kicker can kick the ball 30 m/s at an angle of 30 degrees w.r.t. the ground. If the crossbar of the goal post is 3m off the ground, from how far away can he kick a field goal? y-direction v oy = v o sin(30 o ) = 15 m/s y = y o + v oy t + ½ at 2 3 m = 0 m + (15 m/s) t – ½ (9.8 m/s 2 ) t 2 t = 2.8 s or t = 0.22 s. x-direction v ox = v o cos(30 o ) = 26 m/s D = x o + v ox t + ½ at 2 = 0 m + (26 m/s)(2.8 s) + 0 m/s 2 (2.8 s ) 2 = 72.8 m D 3 m y x Illini Kicks 70 yard Field Goal

39. Mechanics Lecture 2, Slide 38 Vectors and 2d-kinematics – Main Points

40. Vectors and 2d-kinematics Important Equations Mechanics Lecture 2, Slide 39

41. Hyperphysics-Trajectories Mechanics Lecture 1, Slide 40 http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html

42. Hyperphysics-Trajectories Mechanics Lecture 1, Slide 41

43. Hyperphysics-Trajectories Mechanics Lecture 1, Slide 42