Chapter 3: Two Dimensional Motion and Vectors

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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
• Examples
• 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 friends
house (a) then from his friends 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
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??

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Find the direction

• Cant say its just NE because we dont 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 80.54
  North of East

T9.46
T80.54