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Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem.

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Presentation on theme: "Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem."— Presentation transcript:

1 Day 14, Tuesday, 15 September, 2015 Vector Problems Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem Law of Cosines Resolving Components Angle of a Resultant:tan -1 Θ Problem page 75

2 In summary: In an equation or operation with a scalar or dot product, the answer is a scalar quantity that is the product of two vectors. The dot product is found by multiplying the components of vectors that are in the same direction. ABcosΘ In an equation or operation with a vector or cross product, the answer is a vector quantity that is the product of two vectors. The cross product is found by multiplying the components of vectors that are perpendicular to each other. ABsinΘ

3 Vocabulary Speed is a scalar with magnitude only Velocity is a vector with magnitude and direction w r t means with respect to

4 Lecture- Vectors Graphical representation Resultant Addition Subtraction Reference Angle Sin, Cos, Tan Pythagorean Theorem Law of Cosines Resolving Components Angle of a Resultant:tan -1 Θ Problem page 75

5 Graphical representation Arrows Can slide around Cannot change direction Cannot change length Add tip to tail

6 Resultant

7 Addition

8 Addition of several vectors

9 Subtraction

10 Reference Angle Always in Quadrant I

11 Sin, Cos, Tan Sine= sin = opp/hyp Cosine= cos = adj/hyp Tangent = tan = sin/cos = opp/adj

12 Complimentary Angles Complimentary angles make other angles feel good about themselves

13 Pythagorean Theorem R 2 = A 2 + B 2 Works only for 90 º angle

14 Pythagorean Theorem

15 Law of Cosines R 2 = A 2 + B 2 – 2AB cos Θ Works for any angle

16 Resolving Components x = r cos Θ y = r sin Θ

17 Angle of a Resultant: tan -1 Θ

18 Typical Vector Problems 1. Walking home 2. Boat on a river 3. Three vectors

19 Chapter 3 Problems

20 Credits Reference Angle www.netcomuk.co.u Complimentary Angles Cartoon www.cartoonstock.com Vector Addition and Subtraction Wikipedia

21 Credits II Vector Sliding and Multiple Additions www.physics.uoguelph.ca Resultant www.mathwarehouse.com

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