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

2. 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?

3. 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)

4. 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

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

6. 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

7. 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

8. 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

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

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

11. 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

12. 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?

13. 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=?

14. 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

15. 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 °