1 / 19

Introduction to Vectors

Introduction to Vectors. 3.1 pp. 84-87 Mr. Richter. Agenda. Warm-Up A word about yesterday’s test College! Introduction to Two-Dimensional Motion Notes: Scalars and Vectors Adding Vectors Properties of Vector Addition Scaling Vectors Some time in class tomorrow to work on lab report.

conner
Download Presentation

Introduction to Vectors

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Introduction to Vectors 3.1 pp. 84-87 Mr. Richter

  2. Agenda • Warm-Up • A word about yesterday’s test • College! • Introduction to Two-Dimensional Motion • Notes: • Scalars and Vectors • Adding Vectors • Properties of Vector Addition • Scaling Vectors • Some time in class tomorrow to work on lab report.

  3. Objectives: We Will Be Able To… • Distinguish between a scalar and a vector. • Add and subtract vectors using the graphical method. • Multiply and divide vectors by scalars.

  4. Warm-Up: • If a dog walks 4 m east and then 3 m north, how far away is the dog from where it started?

  5. Scalars and Vectors

  6. Scalars and Vectors • Physical quantities can be divided into two quantities: scalars and vectors. • A scalar is a physical quantity that has only magnitude (size). • speed, volume, temperature, etc. • A vector is a physical quantity that has both magnitude and direction. • velocity, acceleration, force, etc.

  7. Vectors • In a diagram, vectors are represented as arrows. • The direction the arrow points indicates the direction of the vector quantity (i.e. velocity, etc.) • The length of the arrow indicates the magnitude of the vector. • short arrows = small magnitudes • long arrows = large magnitudes North East 3 m/s 9 m/s

  8. Vector Addition

  9. Vector Addition • If two or more vectors represent the same quantity, they can be added. • The sum of two or more vectors is called the resultant.

  10. Vector Addition in One Dimension • In one dimension, vector addition is simple addition and subtraction. • A motorboat engine powers the boat to a velocity of 8 m/s north, but the current of the river is 2 m/s south. 2 m/s South 8 m/s North 6 m/s North Resultant 8 + (-2) = 6

  11. Vector Addition in Two Dimensions • In two dimensions, vectors can still be added but the addition looks a little different • A motorboat engine powers the boat to a velocity of 8 m/s north, but the current of the river is 2 m/s east. 2 m/s East 8.2 m/s Resultant 8 m/s North

  12. Vector Addition in Two Dimensions • To find the resultant of vector addition in two dimensions, use graph paper. • Pick a scale, and use a ruler to measure the length of vectors and measure the length of the resultant. • Using a ruler and graph paper, find the magnitude of the resultant vector of a man who walks 42 meters west and 26 meters north. • ~49 meters

  13. Properties of Vectors Addition and Multiplication

  14. Properties of Vector Addition • Vectors can be moved parallel to themselves in a diagram. = This is known as the triangle method of vector addition, or tip-to-tail method

  15. Properties of Vector Addition • Vectors can be added in any order. A + B B + A A A A B B B

  16. Properties of Vector Addition • To subtract a vector, add its opposite -B A A A + (-B) B

  17. Properties of Vector Multiplication • When vector quantities are scaled, their magnitudes are increased or decreased by a factor. • For example, a runner moving three times as fast as before. vrunner = 3 m/s east 3vrunner = 3(3 m/s) = 9 m/s east

  18. Wrap-Up: Did we meet our objectives? • Distinguish between a scalar and a vector. • Add and subtract vectors using the graphical method. • Multiply and divide vectors by scalars.

  19. Homework • p87 #1-5

More Related