1. Vectors

2. Vectors Has both Magnitude and Direction Example:
“A bag of candy is located outside the classroom. To find it, displace yourself 20 meters.”
What’s the problem?

3. How about… “A bag of candy is located outside the classroom
How about… “A bag of candy is located outside the classroom. To find it displace yourself from the center of the classroom door 20 meters in a direction 30 degrees to the west of north.”

4. Scale Vector arrow Magnitude and direction
Vector Diagrams
Scale
Vector arrow
Magnitude and direction
20 m,
30 degrees West of North

5. Vectors are expressed as a counterclockwise angle of rotation

6. Magnitude of a Vector
Using the scale (1 cm = 5 miles), a displacement vector that is 15 miles will be represented by a vector arrow that is 3 cm in length. Similarly, a 25-mile displacement vector is represented by a 5-cm long vector arrow. And finally, an 18-mile displacement vector is represented by a 3.6-cm long arrow. See the examples shown below.

7. Adding Vectors

10. Example…
Eric leaves the base camp and hikes 11 km, north and then hikes 11 km east. Determine Eric's resulting displacement.

12. Practice A Answer
R2 = (5)2 + (10)2
R2 = 125
R = 11.2 km

13. Practice B Answer
R2 = (30)2 + (40)2
R2 = 2500
R = 50 km

14. Using Trig to Determine a Vector’s Direction

15. Stupid Ways, Important Stuff
Sin = o/h
Cos = a/h
Tan = o/a

16. Remember the hiker problem from before?

19. Practice A Tan Ɵ = (5/10) = 0.5 Ɵ = tan-1 (0.5) Ɵ = 26.6 °
Direction of R = 90 ° °
Direction of R = °

20. Practice B Tan Ɵ = (40/30) = 1.333 Ɵ = tan-1 (1.333) Ɵ = 53.1 °
Direction of R = 180 ° °
Direction of R = °