1. Chapter 3 Review Two-Dimensional Motion

2. Essential Question(s):  How can we describe the motion of an object in two dimensions using the one-dimensional concepts of displacement, velocity, and acceleration?

3. Upcoming Schedule  Today: 3.1-3.2 Vectors and Trigonometry  Tomorrow: 3.3-3.4 Projectile and Relative Motion  Monday: 4.1-4.3 Newton’s Laws  Tuesday: 4.4 Everyday Forces (friction and inclined planes!)  Wednesday: Last day of review!  Thursday: Semester Exam.

4. Objective(s):  Add vectors graphically and algebraically.  Determine components of vectors.  Calculate displacement, velocity and acceleration of objects moving in two dimensions.  Describe the motion of objects in different frames of reference.

5. Agenda:  Have a half sheet of paper!  Thursday:  Vectors and Scalars  Adding and Subtracting Vectors Graphically  Determining Algebraic Components of Vectors  Adding and Subtracting Vectors Algebraically  Friday  Projectile Motion  launched horizontally  launched at an angle  Relative Motion

6. What are Vectors?  Vector: a physical quantity that has both a magnitude and a direction.  Example: Velocity  22 m/s North  Scalar: a physical quantity that can be completely described by its magnitude (number and units).  Example: Speed  22 m/s

7. How to Add Vectors  Vectors may be moved parallel to themselves in any diagram.  Vectors can be added in any order.  To subtract a vector, add its opposite.

8. Adding Perpendicular Vectors: Magnitude Use the Pythagorean Theorem For example: use the Pythagorean theorem to find the magnitude of the displacement given its horizontal and vertical components

9. Adding Perpendicular Vectors: Direction Use the inverse tangent function of your calculator Remember: This only tells you the angle, not the direction relative to North or the horizon

10. Your Turn: Adding Perpendicular Vectors  A student walks 4.0 m South and then 9.0 m East. What is the student’s displacement vector? Magnitude: d 2 = 9.0 2 + 4.0 2 = 81.0 + 16.0 d 2 = 97.0 d = √97.0 = 9.8 m Direction: tan θ = 9.0/4.0 = 2.25 θ = tan -1 (2.25) θ = 66° Displacement vector: 9.8 m at 66° E of S

11. Resolving Vectors into Components  In other words  Opp = hyp * sin θ  Adj = hyp * cos θ

12. Your Turn: Resolving Vectors into Components  Find the component velocities of a helicopter traveling at 95 km/h at an angle of 35° to the ground.

13. Adding Non-Perpendicular Vectors 1. Resolve all vectors into horizontal and vertical components. 2. Add components to find total horizontal and vertical components of resultant. 3. Calculate magnitude and direction of resultant.  Try adding 40.0 m at 20.0° below the horizontal and 100.0 m at 35° above the horizontal.

14. Homework  p 97 Section Review  #2 (adding perpendicular vectors)  #3 (finding vector components)  #4 (adding non-perpendicular vectors)