1. Ch2 1-d Kinematics, Problem Solving Consider a real physical situation: I am standing right here and I throw a ball down at the floor. How long until it strikes the second time? Do you know the answer? How do you begin? Let’s do it 2-stage, 2-object problem Solution Physical Situation Interpretation Representation

2. Ch2 Problem Solving The toolbox… Eliminate t Eliminate a Eliminate x… 2.43 2-stage 2.77 2-object problem

3. Ch1 Vectors How can we condense the mathematics? What is a vector? What is an example of a vector quantity? How many different ways can you represent a vector? What is a unit vector? How do find the components of a vector? How do you add vectors? How do vectors do the book keeping? What is the vector form of the kinematic equations?

4. Ch1

5. How do we make this more precise (quantitative)? Ch1

6. Origin Units Axes

7. Ch1 Origin Units Axes

8. Ch1

12. Dot (Scalar) Product Visual representation Meaning, physical quantities? Magnitude No direction By components Magnitude and direction FOIL unit vectors Examples and special cases Ch1

13. Cross (Vector) Product Visual representation Meaning, physical quantities? Magnitude Direction By components (Determinates) Magnitude and direction (RHR) FOIL unit vectors Examples and special cases Ch1

14. Vector Lessons Visual representations are conceptually useful but quantitatively imprecise A vector itself is independent of our choice of coordinate system; it’s components depend on our choice of coordinate system Some choices are more useful than others Unit vectors help quantitatively define coordinate systems Algebraically, we add vectors by adding similar components Dot products measure how parallel two vectors are Cross (vector) products measure how perpendicular two vectors are Although we have to imagine and choose many things in order to solve a a problem, its ultimate physical meaning is the same! What is the vector form of the kinematic equations? Pictures? Ch1