1. Physics 218, Lecture VI1 Physics 218 Lecture 6 Dr. David Toback

2. Physics 218, Lecture VI2 Chapter 4, continued Kinematics in Two Dimensions Today  Problems

3. Physics 218, Lecture VI3

4. 4 Projectile Motion The physics of the universe: The horizontal and vertical Equations of Motion behave independently This is why we use vectors in the first place

5. Physics 218, Lecture VI5 Projectile Motion This is the heart and culmination of what we have learned so far You can rest assured there will be a problem like one in lecture today on the exam

6. Physics 218, Lecture VI6 How to use the Tricks and Methods Next we’ll do an example problem like one of the homework problems in the text book Solve this problem using the right method –Draw a diagram –Convert the numbers to variables –Solve to get a formula –Plug in the numbers at the end –Check Reasonable numbers? Silly numbers? Another way to do the same problem?

7. Physics 218, Lecture VI7 How to Solve Problems The trick for all these problems is to break them up into the X and Y directions

8. Physics 218, Lecture VI8 Firing up in the air at an angle A ball is fired up in the air with speed V o and angle  o. Ignore air friction. The acceleration due to gravity is g pointing down. What is the final velocity here?

9. Physics 218, Lecture VI9 Important Definition ;-) Word: Defenestration Definition: The act of throwing someone or something out of a window

10. Physics 218, Lecture VI10 Push BEVO out of a window Reveille pushes BEVO directly out of a window that is a height h above the ground. Two Aggies observe that BEVO hits the ground a distance D from the base of the building. Assuming BEVO was moving horizontally at the top (and ignoring air friction), how fast must Reveille have pushed her? h D y=0

11. Physics 218, Lecture VI11 Kick a football A football is kicked at angle  with respect to the ground with speed V 0. Calculate: a)The maximum height b)The velocity at the maximum height c)The time of travel before the football hits the ground d)How far away it hits the ground e)What angle maximizes the distance traveled Assume the ball leaves the foot at ground level and ignore air resistance

12. Physics 218, Lecture VI12 Winner: Not my job award

13. Physics 218, Lecture VI13 More Realistic Punt A football is kicked at angle  0 with a speed V 0. The ball leaves the punters foot h meters above the ground. How far does it travel, in the X direction, before it hits the ground? h

14. Physics 218, Lecture VI14 Rescue Plane You are the pilot of a rescue plane and you are flying a plane with a horizontal speed of V p. Your mission is to drop supplies for some mountain climbers on a ridge a vertical distance h below. To do this you have to release the supplies a horizontal distance R in advance of the mountain climbers. What vertical velocity should you give the supplies so that they arrive precisely at the the climbers position?

15. Physics 218, Lecture VI15 Next Week New Material: Not on the 1 st exam Chapter 5: Read for Next time –Newton’s Laws of Motion –HW2 due Monday Cover CH. 3&4 in recitation, due the following Monday Lab 3 (posted on the website)

16. Physics 218, Lecture VI16

17. Physics 218, Lecture VI17 Next time… Reading: None, you’ve already finished Chapter 3 & 4 already Homework: –HW1 was due yesterday –HW2 covered in recitation this week; due this coming Monday –Start working on HW for Chap 3 & 4 Next time: More on kinematics in two dimensions

18. Physics 218, Lecture VI18 Ball Dropping Analyze Vertical and Horizontal separately!!! A y = g (downwards) A x = 0 –Constant for Both cases!!! V x = 0V x >0

19. Physics 218, Lecture VI19 A weird consequence Prove that an object projected horizontally will reach the ground at the same time as an object dropped vertically

20. Physics 218, Lecture VI20 Firing up in the air at an angle A ball is fired up in the air with velocity V o and angle  o. Ignore air friction. The acceleration due to gravity is g pointing down. What is the final velocity here?

21. Physics 218, Lecture VI21 Rescue Plane You are the pilot of a rescue plane. Your mission is to drop supplies to isolated mountain climbers on a rocky ridge a height h below. If your plane is traveling horizontally with a speed of V O : a)How far in advance of the recipients (horizontal distance) must the goods be dropped?

22. Physics 218, Lecture VI22 Rescue Plane cont. b)Suppose instead, that your plane can’t get to that position. Instead you must release the supplies a horizontal distance D in advance of the mountain climbers. What vertical velocity should you give the supplies so that they arrive precisely at the the climbers position. c)What is the speed of the supplies as they hit the ground?

23. Physics 218, Lecture VI23 Announcements: Exam 1 We will move the date of Exam 1 from Tuesday Feb 11 th. Next week you need to do the reading for Chapter 4, Chapter 3-9 and Chapter 5. There will be quizzes on both. Note: You will get recitation on Chapter 3 and turn in your Homework before the exam.

24. Physics 218, Lecture VI24 Next Week Chapter 4: (NOT ON 1 st EXAM) –Dynamics –Newton’s Laws of Motion Finish HW3. Labs & Rec/Web as usual Exam Thursday: Here during regular time –Bring a calculator and ruler –Formula sheet will be provided (on the web already) –Will cover: Chapter 1 (1-6) Calculus 1 Chapter 2 (1-7) Chapter 3 (1-8, 10)

25. Physics 218, Lecture VI25 Example: 3-8 Derive a formula for the horizontal range, R, of a projectile in terms of its initial velocity (v 0 &  ) before the projectile travels before returning to its original height