# Chapter 3: Two Dimensional Motion and Vectors

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Chapter 3: Two Dimensional Motion and Vectors
(Now the fun really starts)

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?

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)

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

Vectors are represented by symbols
Book uses boldface type to indicate vectors Scalars are designated with italics Use arrows to draw vectors

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

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

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

Properties of vectors Vectors can be added in any order
To subtract a vector add its opposite

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

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

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?

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=?

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

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 °