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**Chapter 3: Two Dimensional Motion and Vectors**

(Now the fun really starts)

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**Opening Question I want to go to the library. How do I get there?**

Things I need to know: How far away is it? In what direction(s) do I need to go?

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**One dimensional motion vs two dimensional motion**

One dimensional motion: Limited to moving in one dimension (i.e. back and forth or up and down) Two dimensional motion: Able to move in two dimensions (i.e. forward then left then back)

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Scalars and Vectors Scalar: A physical quantity that has magnitude but no direction Examples: Speed, Distance, Weight, Volume Vector: A physical quantity that has both magnitude and direction Velocity, Displacement, Acceleration

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**Vectors are represented by symbols**

Book uses boldface type to indicate vectors Scalars are designated with italics Use arrows to draw vectors

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**Vectors can be added graphically**

When adding vectors make sure that the units are the same Resultant vector: A vector representing the sum of two or more vectors

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**Adding Vectors Graphically**

Draw situation using a reasonable scale (i.e. 50 m = 1 cm) Draw each vector head to tail using the right scale Use a ruler and protractor to find the resultant vector

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Example: p. 85 in textbook A student walks from his house to his friend’s house (a) then from his friend’s house to school (b). The resultant displacement (c) can be found using a ruler and protractor

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**Properties of vectors Vectors can be added in any order**

To subtract a vector add its opposite

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Coordinate Systems To perform vector operations algebraically we must use trigonometry SOH CAH TOA Pythagorean Theorem:

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**Vectors have directions**

North East of North North of East East West of North South of West South of East East of South West of South North of West West South

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Examples p. 91 #2 While following directions on a treasure map, a pirate walks 45.0 m north then turns around and walks 7.5 m east. What single straight-line displacement could the pirate have taken to reach the treasure?

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**Solving the problem Use the Pythagorean theorem**

R2 = (7.5 m)2 + (45m) 2 R= 45.6 m… What are we missing?? 7.5 m east 45 m N Resultant=?

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Find the direction 45 m N 7.5 m east Resultant=? Can’t say it’s just NE because we don’t know the value of the angle Find the angle using trig

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**What is the angle? (Make sure your calculator is in Deg not Rad)**

Use inverse tangent Final Answer: 46.5 m at 9.46° East of North or 46.5 m at ° North of East 45 m N 7.5 m east Resultant=46.5 m Θ=9.46° Θ=80.54 °

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