Evans SPH 3U1

Physics Grade 11

Unit 1: Forces and Motion

Note 6: Motion in Two Dimensions


Reference: Chapter 2.1, 2.2


Vector Direction Notations:


        tail                          head or tip

   1)   [N60E]   [E30N]    some books will also call these the following (but I do not like).......[30 N of E]    [60 E of N]

   2)   [W60S]  [S30W]   some books will also call these the following (but I do not like).......[30 W of S]    [60 S of W]


    Note:     In words [N60E] reads as "north 60 degrees east"

                 In words [30 N of E] reads as "30 degrees north of east" (but I will not use this one although you should be familiar with it)


Adding Vectors:

Vectors are added tip(head) to tail. The resultant vector is drawn from the tail of the first vector to the head of the last vector. Fig. 3.5 pg.79


Subtracting Vectors:

Subtracting is really the same as adding. i.e. Show example


If you need to add more than two vectors you should use the component method.............



Review trig ratios sine, cosine, tangent (overheads)

Adding with components:

- Resolve vectors into x (horizontal) and y (vertical) components

- Assign directions

- Add horizontal (x) components

- Add vertical (y) components

- Use pythagorean theorem to find the MAGNITUDE of the resultant i.e.

- Use trig ratio to find the DIRECTION of the resultant


Example 1: A student walks 5.0 km [N30E], then 4.0 km [S40E] and then 2.0 km [W]. What is the student's resultant displacement?

Example 2: If the student took 2.5 hours for the trip, what was her speed and velocity?


Adding with Cosine Law and Sine Law:

Pg 65 #8 (scaled)

Pg 75 #1-3

Pg 75 #4,5,6 (components and cosine/sine law)    #7 (components)

Pg 75 #8,9

Handout Motion in 2D