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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.

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Introduction to Vectors

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  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

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