1. Chapter 2 : Kinematics in Two Directions 2.1 Distance & Displacement

2. Quick Trig Review x
5.0 cm
45o

3. Vector Diagrams Several arrows drawn together is a vector diagram
RULES
Vector is drawn in the direction of the vector (object moving EAST, arrow points EAST)
Length of the vector is proportional to magnitude (6 m line longer than a 1m line)
Vectors can be moved as long as they remain the same size and pointing same direction

4. Vectors in ONE dimension
Draw vector diagrams TAIL TO TIP
Example 1: Sketch a diagram which shows how you would add the vectors. A B OR
Resultant of A + B
Resultant of B + A

5. Vectors in ONE dimension
Example 2: Sketch a vector diagram of A – B (which is the same as A + -B) A B
Resultant

6. Vectors in TWO dimensions
Scale Diagram Method
Draw a diagram to solve the problem
Example 3: A man walks 20 metres North and then 50 m West.
a. What is the distance travelled?
b. What is the displacement of the man?

7. Vectors in TWO dimensions
Trigonometry Method
Make a small sketch of the information drawing tail to tip method
Label sketch
Solve for what is missing

8. Vectors in TWO dimensions
Example 4: A man walks 20 metres North and then 50 m West. b. What is the displacement of the man?
50 m
20 m x

9. Vectors in TWO dimensions
Vector Directions
Angles don’t tell you ENOUGH (20o WHERE?)
Cartesian Method
90o
180o 0o
270o

10. Vectors in TWO dimensions
Navigator Method
Use NEWS compass system and measure how many degrees toward one of the other compass points you moved
Two styles of writing answers (VERY DIFFERENT) N W E S

11. N
Example 5: Determine the direction of the vector shown to the left. OR
30o W E
EAST as REFERENCE
Heading counter clockwise a little towards NORTH
[E60oN] S
NORTH as REFERENCE
Heading clockwise a little bit towards EAST
[N30oE]

12. EAST as REFERENCE NORTH as REFERENCE
Example 5: Determine the direction of the vector shown to the left.
30o W E
EAST as REFERENCE
[60o N of E] S
NORTH as REFERENCE
[30o E of N]

13. Already found his DISPLACEMENT, finish it off with direction.x

14. Make SURE your
calculator is in
DEGREE MODE

15. Vectors in TWO dimensions
Example 6: Shandi the seawoman sets sail for Hawaii and heads 12 km East and then 16 km North.
What is Shandi’s distance travelled?
What is Shandi’s displacement?

16. Vectors in TWO dimensions
Example 7: Brandon decides to set sail from Tahiti moving 8 km West and then 17 km South.
What is Brandon’s distance travelled?
What is Brandon’s displacement from Tahiti?

17. Vectors in TWO dimensions
Example 8: Ariel the mermaid decides to do a little swimming. Leaving from the coast of Nova Scotia she heads 14 km East, then 32 km North, then 7 km East and then 8 km South.
What is Ariel’s distance travelled?
What is Ariel’s displacement from Nova Scotia?

18. Vectors in TWO dimensions
Example 9: Calahan the super sea dog decides to go the distance. Calahan heads out from the tip of an arctic island and sails North 14 km. Calahan then omves 12 km East, 8 km North, 5 km West, 24 km South, 7 km West and 3 km North.
What is Calahan’s distance travelled?
What is Calahan’s displacement from the tip of the arctic island?