Chapter 2 : Kinematics in Two Directions 2.1 Distance & Displacement

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Chapter 2 : Kinematics in Two Directions 2.1 Distance & Displacement

Quick Trig Review x 5.0 cm 45o

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

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

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

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?

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

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

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

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

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]

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]

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

Make SURE your calculator is in DEGREE MODE

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?

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?

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?

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?