1. © 2010 Pearson Education, Inc. Lecture Outline Chapter 3 College Physics, 7 th Edition Wilson / Buffa / Lou

2. Chapter 3 Motion in Two Dimensions © 2010 Pearson Education, Inc.

3. Units of Chapter 3 Components of Motion Vector Addition and Subtraction Projectile Motion Relative Velocity © 2010 Pearson Education, Inc.

4. 3.1 Components of Motion An object in motion on a plane can be located using two numbers—the x and y coordinates of its position. Similarly, its velocity can be described using components along the x - and y -axes. © 2010 Pearson Education, Inc.

5. 3.1 Components of Motion The velocity components are: The magnitude of the velocity vector is: © 2010 Pearson Education, Inc.

6. 3.1 Components of Motion The components of the displacement are then given by: Note that the x- and y- components are calculated separately. © 2010 Pearson Education, Inc.

7. 3.1 Components of Motion The equations of motion are: When solving two-dimensional kinematics problems, each component is treated separately. The time is common to both. © 2010 Pearson Education, Inc.

8. 3.1 Components of Motion If the acceleration is not parallel to the velocity, the object will move in a curve: © 2010 Pearson Education, Inc.

9. 3.2 Vector Addition and Subtraction Geometric methods of vector addition Triangle method: © 2010 Pearson Education, Inc.

10. 3.2 Vector Addition and Subtraction The negative of a vector has the same magnitude but is opposite in direction to the original vector. Adding a negative vector is the same as subtracting a vector. © 2010 Pearson Education, Inc.

11. 3.2 Vector Addition and Subtraction Vector Components and the Analytical Component Method If you know A and B, here is how to find C: © 2010 Pearson Education, Inc.

12. 3.2 Vector Addition and Subtraction The components of C are given by: Equivalently, © 2010 Pearson Education, Inc.

13. 3.2 Vector Addition and Subtraction Vectors can also be written using unit vectors: © 2010 Pearson Education, Inc.

14. 3.2 Vector Addition and Subtraction Vectors can be resolved into components and the components added separately; then recombine to find the resultant. © 2010 Pearson Education, Inc.

15. 3.2 Vector Addition and Subtraction This is done most easily if all vectors start at the origin. © 2010 Pearson Education, Inc.

16. 3.3 Projectile Motion An object projected horizontally has an initial velocity in the horizontal direction, and acceleration (due to gravity) in the vertical direction. The time it takes to reach the ground is the same as if it were simply dropped. © 2010 Pearson Education, Inc.

17. 3.3 Projectile Motion A projectile launched in an arbitrary direction may have initial velocity components in both the horizontal and vertical directions, but its acceleration is still downward. © 2010 Pearson Education, Inc.

18. 3.3 Projectile Motion The vertical motion is the same as if the object were thrown straight up or down with the same initial y velocity, and the horizontal velocity is constant. © 2010 Pearson Education, Inc.

19. 3.3 Projectile Motion The range of a projectile is maximum (if there is no air resistance) for a launch angle of 45°. © 2010 Pearson Education, Inc.

20. 3.3 Projectile Motion With air resistance, the range is shortened, and the maximum range occurs at an angle less than 45°. © 2010 Pearson Education, Inc.

21. 3.4 Relative Velocity Velocity may be measured in any inertial reference frame. At top, the velocities are measured relative to the ground; at bottom they are measured relative to the white car. © 2010 Pearson Education, Inc.

22. 3.4 Relative Velocity In two dimensions, the components of the velocity, and therefore the angle it makes with a coordinate axis, will change depending on the point of view. © 2010 Pearson Education, Inc.

23. Review of Chapter 3 Two-dimensional motion is analyzed by considering each component separately. Time is the common factor. © 2010 Pearson Education, Inc.

24. Review of Chapter 3 Vector components: In projectile motion, the horizontal and vertical motions are determined separately. © 2010 Pearson Education, Inc.

25. Review of Chapter 3 Range is the maximum horizontal distance traveled. Relative velocity is expressed relative to a particular reference frame. © 2010 Pearson Education, Inc.