1. Physics 218, Lecture V1 Physics 218 Lecture 5 Dr. David Toback

2. Physics 218, Lecture V2 Notes Updated Class Schedule on my web page –New lab assignments/dates –New reading/chapter assignments (i.e., what we are doing each week) End of Chapter quizzes coming soon. Will let you know when they are posted

3. Physics 218, Lecture V3 Checklist for Today Things that were due last Thursday: –Chapter 2 reading –Read all handouts from web page Things that are due yesterday (Monday): –WebCT Prelim (FCI, Math Assess, etc…) –Math Quizzes 1 through 10 Things that are due today: –Reading for Chapters 3 & 4 For this week and/or due next Monday: –Recitation: Start Ch. 2 on WebCT –All HW2 problems on WebCT due Monday

4. Physics 218, Lecture V4 This Week Chapters 3 and 4 –Vectors and Two Dimensional Motion –Do these two chapters together Vectors Position, Velocity and Acceleration Projectile Motion

5. Physics 218, Lecture V5

6. 6

7. 7 Vectors Why we care about them Addition & Subtraction

8. Physics 218, Lecture V8 Why do we care about Vectors? As you may have noticed, the world is not one-dimensional Three dimensions: X, Y and Z. Example: 1.Up from us 2.Straight in front of us 3.To the side from us –All at 90 degrees from each other. Three dimensional axis. Need a way of saying how much in each direction For this we use VECTORS

9. Physics 218, Lecture V9 Vector and Scalar Vectors have a magnitude AND a direction –I’m driving 70 miles/hr SouthEast to Houston Scalars are just a number –My speedometer says 70 m/hr

10. Physics 218, Lecture V10 Where am I? My single vector in some funny direction, can be thought of as two vectors in nice simple directions (like X and Y). This can make things much easier Let’s say I’m here You’re here (origin) I call you on the cell phone. How do I tell you how to get to me? 2 equivalent ways: 1)Travel 11.2 km at an angle of 26.5 degrees 2)Travel 10 km East then 5 km North

11. Physics 218, Lecture V11 Re-write my location Describe my location in terms of the sum of two vectors Careful when using the sin and cos

12. Physics 218, Lecture V12 Specifying a Vector Two equivalent ways: –Components V x and V y –Magnitude V and angle  Switch back and forth –Magnitude of V |V| = (v x 2 + v y 2 ) ½ Pythagorean Theorem –Tan  = v y /v x Either method is fine, but you should pick which is easiest, and be able to use both

13. Physics 218, Lecture V13 Unit Vectors This is how the pros write things!

14. Physics 218, Lecture V14 Unit Vectors The pros also use:

15. Physics 218, Lecture V15 Vector in Unit Vector Notation

16. Physics 218, Lecture V16 General Addition Example Add two vectors using the i- hats and j- hats

17. Physics 218, Lecture V17 Motion in 2-Dimensions Moving from Chapter 3 to Chapter 4 This is what all the setup has been for! Motion in two and three dimensions –For now we’ll ignore air friction

18. Physics 218, Lecture V18 Position in 2 dimensions

19. Physics 218, Lecture V19 Velocity in 2 dimensions

20. Physics 218, Lecture V20 Acceleration in 2 dimensions

21. Physics 218, Lecture V21 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

22. Physics 218, Lecture V22 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?

23. Physics 218, Lecture V23 How to Solve Problems The trick for all these problems is to break them up into the X and Y directions

24. Physics 218, Lecture V24 Ball Dropping Analyze Vertical and Horizontal separately!!! A y = g (downwards) A x = 0 –Constant for Both cases!!! V x = 0V x >0

25. Physics 218, Lecture V25 A weird consequence Prove that an object projected horizontally will reach the ground at the same time as an object dropped vertically

26. Physics 218, Lecture V26 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?

27. Physics 218, Lecture V27 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

28. Physics 218, Lecture V28

29. Physics 218, Lecture V29 Vector Addition To specify where I am, often doing the two vector version is easier Represent Graphically: Lay down first vector Lay down second vector –Put the tail at the head of the first vector The “Sum” is where I am Adding vectors is a skill Use this in far more than just physics More on this later…

30. Physics 218, Lecture V30 Vectors Vectors: –Why we care about them –Addition & Subtraction –Unit Vectors –Multiplication

31. Physics 218, Lecture V31 Position in 3 dimensions

32. Physics 218, Lecture V32 General Addition Example Add two vectors using the i- hats, j-hats and k-hats

33. Physics 218, Lecture V33 Velocity in 3 dimensions

34. Physics 218, Lecture V34 A Mail Carrier A rural mail carrier leaves leaves the post office and drives D 1 miles in a Northerly direction to the next town. She then drives in a direction  degrees South of East for a distance D 2 to another town. What is the magnitude and angle of her displacement from the post office?

35. Physics 218, Lecture V35 Constant Acceleration

36. Physics 218, Lecture V36 Example: Adding Unit Vectors

37. Physics 218, Lecture V37 Vector stuff 1.Pythagorean theorem: We’ll use this a lot –For a right triangle (90 degrees) –Length C is the hypotenuse –A 2 + B 2 = C 2 2.Vector equations

38. Physics 218, Lecture V38 Using all this stuff

39. Physics 218, Lecture V39 Unit Vectors This is how the pros write things!

40. Physics 218, Lecture V40 Unit Vectors The pros also use: