1. Vectors Measured values with a direction
Shown with +/- in each dimension
Shown as arrow for two-dimensions

2. Vectors Measured values with a direction
Shown with +/- in each dimension
Shown as arrow for two-dimensions
Length of arrow represents the size or magnitude of the measurement
5 m/s would be shown with a shorter arrow than 20 m/s

3. Vectors These may only be used for Right Triangle
(a triangle with a right angle)

4. Vectors
The legs are the sides of the triangle that are next to the right angle
The hypotenuse is across from the right angle
It is always the longest side of the triangle

5. Vectors
Hypotenuse
Leg
Leg

6. Vectors c a b

7. Vectors
Pythagorean Theorem – used to find the length of each side of a right triangle
a2 + b2 = c2 c a b

8. Trig Functions
If another angle ( θ ) is known, trig functions can be used c a b θ

9. Vectors c 3 4 10 6 x

10. North:
South:
East:
West:

11. North: up
South: down
East: right
West: left

12. Horizontal vectors
Vertical vectors

13. x-value Horizontal vectors: X-direction Vertical vectors: Y-direction
y-value

15. Vector addition Vector resolution
combining two (or more) vectors to produce a single resultant vector
Vector resolution
showing a single vector as a combination of other vectors (using vector addition)
we will find horizontal and vertical to be the most beneficial components to use

16. As long as both direction (angle) and size (magnitude) of the vector are not changed, they can be moved and rearranged as needed
To show addition, all vectors must be aligned “tip-to-tail”

17. Draw triangles and use trig equations to solve for both vector addition and vector resolution

18. Examples Vector Addition
Show the x-value arrow, then the y-value arrow Remember: tip-to-tail Then show the single arrow that does the same thing
Use Pythagorean Theorem to solve

19. Combine the following vectors:
300 meters south
400 meters west

20. Combine the following vectors:
300 meters south
400 meters west
400 m

21. Combine the following vectors:
300 meters south
400 meters west
400 m
300 m

22. Combine the following vectors:
300 meters south
400 meters west
400 m
400
300 m vT

23. Combine the following vectors: 300 meters south 400 meters westvT
Find vT

24. a2 + b2 = c2
= vT2
vT = 500 meters
400 m
300 m vT

25. a2 + b2 = c2
= vT2
vT = 500 meters
400 m
300 m
500 meters

26. Examples Vector Resolution
Show the single v-arrow and angle with a dotted line Then show the x-arrow and y-arrow that combine tip-to-tail to make up the single v arrow

27. Vector resolution θ

28. Vector resolution θ vx

29. Vector resolution vy θ vx

30. Example

31. Show the horizontal and vertical components of the following vector:
100 30°
30°
100 m/s

32. Show the horizontal and vertical components of the following vector:
100 30° x
30°
100 m/s

33. Show the horizontal and vertical components of the following vector:
100 30° x
30° y
100 m/s

34. Special Triangles a
45° b

35. Special Triangles
Legs are same length with 45° triangle
a = b a
45° b

36. Special Triangles Legs are same length with 45° triangle a = b a 45°

37. Special Triangles Legs are same length with 45° triangle a2 + b2 = c2
a2 + a2 = c2 a
45°
b a

38. Special Triangles Legs are same length with 45° triangle a2 + a2 = c2
b a

39. Complimentary Angles
Two angles that add up to 90°

40. Complimentary Angles Two angles that add up to 90°
The two angles inside a triangle are complimentary

41. Complimentary Angles Two angles that add up to 90°
The two angles inside a triangle are complimentary
When the angles inside are switched, the legs of the right triangle are also switched

42. Complimentary Angles a
30° b

43. Complimentary Angles
60° a
30° b

44. Complimentary Angles
60° a
30° b
60°

45. Complimentary Angles
60° a
30° b
30°
30 and 60 are complimentary
60°

46. Complimentary Angles a
30° b b
60° a