Presentation on theme: "Chapter 3: Two Dimensional Motion and Vectors"— Presentation transcript:
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 VectorsScalar: A physical quantity that has magnitude but no directionExamples:Speed, Distance, Weight, VolumeVector: A physical quantity that has both magnitude and directionVelocity, Displacement, Acceleration
5 Vectors are represented by symbols Book uses boldface type to indicate vectorsScalars are designated with italicsUse arrows to draw vectors
6 Vectors can be added graphically When adding vectors make sure that the units are the sameResultant 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 scaleUse a ruler and protractor to find the resultant vector
8 Example: p. 85 in textbookA 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 SystemsTo perform vector operations algebraically we must use trigonometrySOH CAH TOAPythagorean Theorem:
11 Vectors have directions NorthEast of NorthNorth of EastEastWest of NorthSouth of WestSouth of EastEast of SouthWest of SouthNorth of WestWestSouth
12 Examples p. 91 #2While 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) 2R= 45.6 m…What are we missing??7.5 m east45 mNResultant=?
14 Find the direction45 mN7.5 m eastResultant=?Can’t say it’s just NE because we don’t know the value of the angleFind the angle using trig
15 What is the angle? (Make sure your calculator is in Deg not Rad) Use inverse tangentFinal Answer:46.5 m at 9.46° East of North or 46.5 m at ° North of East45 mN7.5 m eastResultant=46.5 mΘ=9.46°Θ=80.54 °