1. Vector Components

2. Vector Components
Based on the right angle
triangle

3. Vector Components Θ Based on the right angle triangle
Need a reference angle Θ

4. Vector Components Θ Based on the right angle triangle
Need a reference angle
Which sides are the
adjacent, opposite, and hypotenuse? Θ

5. Vector Components Θ H A O Based on the right angle triangle
Need a reference angle H Θ A O

6. Vector Components Θ H A O Based on the right angle triangle
Need a reference angle
O = ​? H H Θ A O

7. Vector Components Θ H A O Based on the right angle triangle
Need a reference angle
O = ​sinΘ H H Θ A O

8. Vector Components Θ H A O Based on the right angle triangle
Need a reference angle
O = ​sinΘ H
O = ? H Θ A O

9. Vector Components Θ H A O Based on the right angle triangle
Need a reference angle
O = ​sinΘ H
O = H sinΘ H Θ A O

10. Vector Components Θ H A O Based on the right angle triangle
Need a reference angle
O = ​sinΘ H
O = H sinΘ Memorize this component equation #1 H Θ A O

11. Vector Components Θ H A O Based on the right angle triangle
Need a reference angle
O = ​sinΘ H
O = H sinΘ Memorize this component equation #1
A = ? H Θ A O

12. Vector Components Θ H A O Based on the right angle triangle
Need a reference angle
O = ​sinΘ H
O = H sinΘ Memorize this component equation #1
A = cosΘ H Θ A O

13. Vector Components Θ H A O Based on the right angle triangle
Need a reference angle
O = ​sinΘ H
O = H sinΘ Memorize this component equation #1
A = cosΘ So A = ? H Θ A O

14. Vector Components Θ H A O Based on the right angle triangle
Need a reference angle
O = ​sinΘ H
O = H sinΘ Memorize this component equation #1
A = cosΘ So A = H cosΘ H Θ A O

15. Vector Components Θ H A O Based on the right angle triangle
Need a reference angle
O = ​sinΘ H
O = H sinΘ Memorize this component equation #1
A = cosΘ So A = H cosΘ Memorize component
H equation #2 H Θ A O

16. Example #1: A plane takes off at 300. 0 km/h at an angle of 36
Example #1: A plane takes off at km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity?

17. Example #1: A plane takes off at 300. 0 km/h at an angle of 36
Example #1: A plane takes off at km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity?
Draw a vector
component diagram.

18. Example #1: A plane takes off at 300. 0 km/h at an angle of 36
Example #1: A plane takes off at km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity?
Draw a vector
component diagram.
300 km/h
Θ=36.9°
Vector Component Diagram

19. Example #1: A plane takes off at 300. 0 km/h at an angle of 36
Example #1: A plane takes off at km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity?
Label A, O, H
300 km/h
Θ=36.9°
Vector Component Diagram

20. Example #1: A plane takes off at 300. 0 km/h at an angle of 36
Example #1: A plane takes off at km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity?
Label A, O, H H
300 km/h O
Θ=36.9° A
Vector Component Diagram

21. Example #1: A plane takes off at 300. 0 km/h at an angle of 36
Example #1: A plane takes off at km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity?
A = component formula? H
300 km/h O
Θ=36.9° A
Vector Component Diagram

22. Example #1: A plane takes off at 300. 0 km/h at an angle of 36
Example #1: A plane takes off at km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity?
A = H cosΘ H
300 km/h O
Θ=36.9° A
Vector Component Diagram

23. Example #1: A plane takes off at 300. 0 km/h at an angle of 36
Example #1: A plane takes off at km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity?
A = H cosΘ
= cos 36.9° H
300 km/h O
Θ=36.9° A
Vector Component Diagram

24. Example #1: A plane takes off at 300. 0 km/h at an angle of 36
Example #1: A plane takes off at km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity?
A = H cosΘ
= cos 36.9°
= 240 H
300 km/h O
Θ=36.9° A
Vector Component Diagram

25. Example #1: A plane takes off at 300. 0 km/h at an angle of 36
Example #1: A plane takes off at km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity?
A = H cosΘ
= cos 36.9°
= 240
O = component formula? H
300 km/h O
Θ=36.9° A
Vector Component Diagram

26. Example #1: A plane takes off at 300. 0 km/h at an angle of 36
Example #1: A plane takes off at km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity?
A = H cosΘ
= cos 36.9°
= 240
O = H sinΘ H
300 km/h O
Θ=36.9° A
Vector Component Diagram

27. Example #1: A plane takes off at 300. 0 km/h at an angle of 36
Example #1: A plane takes off at km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity?
A = H cosΘ
= cos 36.9°
= 240
O = H sinΘ
= 300 sin 36.9° H
300 km/h O
Θ=36.9° A
Vector Component Diagram

28. Example #1: A plane takes off at 300. 0 km/h at an angle of 36
Example #1: A plane takes off at km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity?
A = H cosΘ
= cos 36.9°
= 240
O = H sinΘ
= 300 sin 36.9°
= 180 H
300 km/h O
Θ=36.9° A
Vector Component Diagram

29. Example #1: A plane takes off at 300. 0 km/h at an angle of 36
Example #1: A plane takes off at km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity?
A = H cosΘ
= cos 36.9°
= 240
O = H sinΘ
= 300 sin 36.9°
= 180
State the vector components using symbols with the XY plane as a reference axis. H
300 km/h O
Θ=36.9° A
Vector Component Diagram

30. Example #1: A plane takes off at 300. 0 km/h at an angle of 36
Example #1: A plane takes off at km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity?
A = H cosΘ
= cos 36.9°
= 240
O = H sinΘ
= 300 sin 36.9°
= 180
Vx = +240 km/h = 240 km/h [ forward horizontal ] H
300 km/h O
Θ=36.9° A
Vector Component Diagram

31. Example #1: A plane takes off at 300. 0 km/h at an angle of 36
Example #1: A plane takes off at km/h at an angle of 36.9° to the ground. What are the horizontal and vertical components of the plane's velocity?
A = H cosΘ
= cos 36.9°
= 240
O = H sinΘ
= 300 sin 36.9°
= 180
Vx = +240 km/h = 240 km/h [ forward horizontal ]
Vy = +180 km/h = 180 km/h [ upward vertical ] H
300 km/h O
Θ=36.9° A
Vector Component Diagram

32. Harder Example #1b: A plane takes off at 300. 0 km/h at an angle of 36
Harder Example #1b: A plane takes off at km/h at an angle of 36.9° to the ground. How many minutes does it take to reach an altitude of m?
Vx = +240 km/h = 240 km/h [ forward horizontal ]
Vy = +180 km/h = 180 km/h [ upward vertical ]

33. Harder Example #1b: A plane takes off at 300. 0 km/h at an angle of 36
Harder Example #1b: A plane takes off at km/h at an angle of 36.9° to the ground. How many minutes does it take to reach an altitude of m?
t = Δd/vy
= m/ 180 km/h
But m X 1 km/1000 m = km
So t = km / 180 km/h or
= km X (1/180 h/km)
= h
Convert to minutes t = h X 60 min/1 h
= minute

34. Try this example #2: What are the easterly and southerly components of the force 34.0 N [S28.1°E] ?

35. Try this example #2: What are the easterly and southerly components of the force 34.0 N [S28.1°E] ?
A = H cosϴ
= 34 cos 28.1°
= 30.0 N
O = H sinϴ
= 34 sin 28.1°
= 16.0 N
Fx = N = 16.0 N [East]
Fy = N = 30.0 N [south]
ϴ= 28.1° A
34.0 N O

36. Adding Vectors Using the Component Method

37. Adding Vectors Using the Component Method
Can be used to add two or more vectors together

38. Adding Vectors Using the Component Method
Can be used to add two or more vectors together
Example: Find the vector sum of :
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] m/s [W]

39. Adding Vectors Using the Component Method
Can be used to add two or more vectors together
Example: Find the vector sum of :
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Step One

40. Adding Vectors Using the Component Method
Can be used to add two or more vectors together
Example: Find the vector sum of :
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Step One: By drawing vector component diagrams,
find the vector components of any oblique vectors:

41. Adding Vectors Using the Component Method
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Step One: By drawing vector component diagrams,
find the vector components of any oblique vectors:

42. Adding Vectors Using the Component Method
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Step One: By drawing vector component diagrams,
Find the vector components of any oblique vectors: 17
Θ=28.1°

43. Adding Vectors Using the Component Method
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Step One: By drawing vector component diagrams,
find the vector components of any oblique vectors:
A = component formula? 17
Θ=28.1°
A = ?

44. Adding Vectors Using the Component Method
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Step One: By drawing vector component diagrams,
find the vector components of any oblique vectors:
A = H cosΘ 17
Θ=28.1°
A = ?

45. Adding Vectors Using the Component Method
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Step One: By drawing vector component diagrams,
Find the vector components of any oblique vectors:
A = H cosΘ
= 17 cos(28.1°) 17
Θ=28.1°
A = ?

46. Adding Vectors Using the Component Method
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Step One By drawing vector component diagrams,
find the vector components of any oblique vectors:
A = H cosΘ
= 17 cos(28.1°)
= 15.0 17
Θ=28.1°
A = ?

47. Adding Vectors Using the Component Method
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Step One: By drawing vector component diagrams,
find the vector components of any oblique vectors:
A = H cosΘ
= 17 cos(28.1°)
= 15.0
Symbol for west vector component? 17
Θ=28.1°
A = ?

48. Adding Vectors Using the Component Method
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Step One: By drawing vector component diagrams,
Find the vector components of any oblique vectors:
A = H cosΘ
= 17 cos(28.1°)
= 15.0
vx= ? 17
Θ=28.1°
A = ?

49. Adding Vectors Using the Component Method
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Step One: By drawing vector component diagrams,
find the vector components of any oblique vectors:
A = H cosΘ
= 17 cos(28.1°)
= 15.0
Vx= m/s 17
Θ=28.1°
A = ?

50. Adding Vectors Using the Component Method
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Step One By drawing vector component diagrams,
find the vector components of any oblique vectors:
A = H cosΘ O = formula?
= 17 cos(28.1°)
= 15.0
Vx= m/s 17
O=?
Θ=28.1°
A = ?

51. Adding Vectors Using the Component Method
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Step One: By drawing vector component diagrams,
Find the vector components of any oblique vectors:
A = H cosΘ O = H sinΘ
= 17 cos(28.1°)
= 15.0
Vx= m/s 17
O=?
Θ=28.1°
A = ?

52. Adding Vectors Using the Component Method
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Step One: By drawing vector component diagrams,
find the vector components of any oblique vectors:
A = H cosΘ O = H sinΘ
= 17 cos(28.1°) = ?
= 15.0
Vx= m/s 17
O=?
Θ=28.1°
A = ?

53. Adding Vectors Using the Component Method
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Step One: By drawing vector component diagrams,
find the vector components of any oblique vectors:
A = H cosΘ O = H sinΘ
= 17 cos(28.1°) = 17sin(28.1°)
= 15.0
Vx= m/s 17
O=?
Θ=28.1°
A = ?

54. Adding Vectors Using the Component Method
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Step One: By drawing vector component diagrams,
find the vector components of any oblique vectors:
A = H cosΘ O = H sinΘ
= 17 cos(28.1°) = 17sin(28.1°)
= = 8.01
Vx= m/s 17
O=?
Θ=28.1°
A = ?

55. Adding Vectors Using the Component Method
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Step One: By drawing vector component diagrams,
find the vector components of any oblique vectors:
A = H cosΘ O = H sinΘ
= 17 cos(28.1°) = 17sin(28.1°)
= = 8.01
Vx= m/s symbol for north
component =? 17
O=?
Θ=28.1°
A = ?

56. Adding Vectors Using the Component Method
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Step One By drawing vector component diagrams,
find the vector components of any oblique vectors:
A = H cosΘ O = H sinΘ
= 17 cos(28.1°) = 17sin(28.1°)
= = 8.01
Vx= m/s Vy= ? 17
O=?
Θ=28.1°
A = ?

57. Adding Vectors Using the Component Method
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Step One: By drawing vector component diagrams,
find the vector components of any oblique vectors:
A = H cosΘ O = H sinΘ
= 17 cos(28.1°) = 17sin(28.1°)
= = 8.01
Vx= m/s Vy= m/s 17
O=?
Θ=28.1°
A = ?

58. Adding Vectors Using the Component Method
Step One: Use vector component diagrams to find the vector components of any oblique vectors
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s
Vy= m/s

59. Adding Vectors Using the Component Method
Step One By drawing vector component diagrams, find the vector components of any oblique vectors
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s
Vy= m/s
22.6° 13

60. Adding Vectors Using the Component Method
Step One: By drawing vector component diagrams,find the vector components of any oblique vectors
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s
Vy= m/s
A = component formula?
22.6° 13
A=?

61. Adding Vectors Using the Component Method
Step One: By drawing vector component diagrams,find the vector components of any oblique vectors
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s
Vy= m/s
A = HcosΘ
22.6° 13
A=?

62. Adding Vectors Using the Component Method
Step One: By drawing vector component diagrams, find the vector components of any oblique vectors
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s
Vy= m/s
A = HcosΘ
= 13cos(22.6°)
22.6° 13
A=?

63. Adding Vectors Using the Component Method
Step One: By drawing vector component diagrams, find the vector components of any oblique vectors
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s
Vy= m/s
A = HcosΘ
= 13cos(22.6°)
= 12.0
22.6° 13
A=?

64. Adding Vectors Using the Component Method
Step One : By drawing vector component diagrams, find the vector components of any oblique vectors
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s
Vy= m/s
A = HcosΘ
= 13cos(22.6°)
= 12.0
Symbol for south
vector component?
22.6° 13
A=?

65. Adding Vectors Using the Component Method
Step One : By drawing vector component diagrams, find the vector components of any oblique vectors
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s
Vy= m/s
A = HcosΘ
= 13cos(22.6°)
= 12.0
Vy = ?
22.6° 13
A=?

66. Adding Vectors Using the Component Method
Step One : By drawing vector component diagrams, find the vector components of any oblique vectors
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s
Vy= m/s
A = HcosΘ
= 13cos(22.6°)
= 12.0
Vy = m/s
22.6° 13
A=?

67. Adding Vectors Using the Component Method
Step One : By drawing vector component diagrams, find the vector components of any oblique vectors
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s
Vy= m/s
A = HcosΘ O = formula ?
= 13cos(22.6°)
= 12.0
Vy = m/s
22.6° 13
A=?
O =?

68. Adding Vectors Using the Component Method
Step One : By drawing vector component diagrams, find the vector components of any oblique vectors
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s
Vy= m/s
A = HcosΘ O = HsinΘ
= 13cos(22.6°)
= 12.0
Vy = m/s
22.6° 13
A=?
O =?

69. Adding Vectors Using the Component Method
Step One : By drawing vector component diagrams, find the vector components of any oblique vectors
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s
Vy= m/s
A = HcosΘ O = HsinΘ
= 13cos(22.6°) = 13sin(22.6°)
= 12.0
Vy = m/s
22.6° 13
A=?
O =?

70. Adding Vectors Using the Component Method
Step One : By drawing vector component diagrams, find the vector components of any oblique vectors
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s
Vy= m/s
A = HcosΘ O = HsinΘ
= 13cos(22.6°) = 13sin(22.6°)
= = 5.00
Vy = m/s
22.6° 13
A=?
O =?

71. Adding Vectors Using the Component Method
Step One : By drawing vector component diagrams, find the vector components of any oblique vectors
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s
Vy= m/s
A = HcosΘ O = HsinΘ
= 13cos(22.6°) = 13sin(22.6°)
= = 5.00
Vy = m/s symbol for east
vector component ?
22.6° 13
A=?
O =?

72. Adding Vectors Using the Component Method
Step One : By drawing vector component diagrams, find the vector components of any oblique vectors
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s
Vy= m/s
A = HcosΘ O = HsinΘ
= 13cos(22.6°) = 13sin(22.6°)
= = 5.00
Vy = m/s Vx= ?
22.6° 13
A=?
O =?

73. Adding Vectors Using the Component Method
Step One : By drawing vector component diagrams, find the vector components of any oblique vectors
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s
Vy= m/s
A = HcosΘ O = HsinΘ
= 13cos(22.6°) = 13sin(22.6°)
= = 5.00
Vy = m/s Vx= m/s
22.6° 13
A=?
O =?

74. Adding Vectors Using the Component Method
Step Two: Set up a chart listing the x and y components
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s Vx= m/s Vx= ? Vx= ?
Vy= m/s Vy = m/s Vy= ? Vy= ?

75. Adding Vectors Using the Component Method
Step Two: Set up a chart listing the x and y components
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s Vx= m/s Vx= 0 m/s Vx= ?
Vy= m/s Vy = m/s Vy= ? Vy= ?

76. Adding Vectors Using the Component Method
Step Two: Set up a chart listing the x and y components
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s Vx= m/s Vx= 0 m/s Vx= ?
Vy= m/s Vy = m/s Vy= ? Vy= ?

77. Adding Vectors Using the Component Method
Step Two: Set up a chart listing the x and y components
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s Vx= m/s Vx= 0 m/s Vx= ?
Vy= m/s Vy = m/s Vy= m/s Vy= ?

78. Adding Vectors Using the Component Method
Step Two: Set up a chart listing the x and y components
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s Vx= m/s Vx= 0 m/s Vx= -8.0 m/s
Vy= m/s Vy = m/s Vy= m/s Vy= ?

79. Adding Vectors Using the Component Method
Step Two: Set up a chart listing the x and y components
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s Vx= m/s Vx= 0 m/s Vx= -8.0 m/s
Vy= m/s Vy = m/s Vy= m/s Vy= 0.m/s

80. Adding Vectors Using the Component Method
Step Two: Set up a chart listing the x and y components
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s Vx= m/s Vx= 0 m/s Vx= -8.0 m/s
Vy= m/s Vy = m/s Vy= m/s Vy= 0.m/s
Step Three: Add the x components and y components

81. Adding Vectors Using the Component Method
Step Two: Set up a chart listing the x and y components
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s Vx= m/s Vx= 0 m/s Vx= -8.0 m/s
Vy= m/s Vy = m/s Vy= m/s Vy= 0.m/s
Step Three: Add the x components and y components
Vx (total) = ?
Vy (total) = ?

82. Adding Vectors Using the Component Method
Step Two: Set up a chart listing the x and y components
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s Vx= m/s Vx= 0 m/s Vx= -8.0 m/s
Vy= m/s Vy = m/s Vy= m/s Vy= 0.m/s
Step Three: Add the x components and y components
Vx (total) = m/s
Vy (total) = ?

83. Adding Vectors Using the Component Method
Step Two: Set up a chart listing the x and y components
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s Vx= m/s Vx= 0 m/s Vx= -8.0 m/s
Vy= m/s Vy = m/s Vy= m/s Vy= 0.m/s
Step Three: Add the x components and y components
Vx (total) = m/s
Vy (total) = m/s

84. Adding Vectors Using the Component Method
Step Two: Set up a chart listing the x and y components
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s Vx= m/s Vx= 0 m/s Vx= -8.0 m/s
Vy= m/s Vy = m/s Vy= m/s Vy= 0.m/s
Step Three: Add the x components and y components
Vx (total) = m/s
Vy (total) = m/s
Step Four: ?

85. Adding Vectors Using the Component Method
Step Two: Set up a chart listing the x and y components
17.0 m/s [W28.1°N] m/s [S22.6°E] m/s [S] +8.0 m/s [W]
Vx= m/s Vx= m/s Vx= 0 m/s Vx= -8.0 m/s
Vy= m/s Vy = m/s Vy= m/s Vy= 0.m/s
Step Three: Add the x components and y components
Vx (total) = m/s
Vy (total) = m/s
Step Four: Draw a tip-to-tail diagram and find the vector sum

86. Adding Vectors Using the Component Method
Step Three: Add the x components and y components
Vx (total) = m/s Vy (total) = m/s
Step Four: Draw a tip-to-tail diagram and find the vector sum

87. Adding Vectors Using the Component Method
Step Three: Add the x components and y components
Vx (total) = m/s Vy (total) = m/s
Step Four: Draw a tip-to-tail diagram and find the vector sum
Note: Just label as positive magnitudes
18.0 m/s

88. Adding Vectors Using the Component Method
Step Three: Add the x components and y components
Vx (total) = m/s Vy (total) = m/s
Step Four: Draw a tip-to-tail diagram and find the vector sum
Note: Just label as positive magnitudes
18.0 m/s
14.0 m/s

89. Adding Vectors Using the Component Method
Step Three: Add the x components and y components
Vx (total) = m/s Vy (total) = m/s
Step Four: Draw a tip-to-tail diagram and find the vector sum
Note: Just label as positive magnitudes
18.0 m/s
14.0 m/s
Vector sum or Vtotal

90. Adding Vectors Using the Component Method
Step Three: Add the x components and y components
Vx (total) = m/s Vy (total) = m/s
Step Four: Draw a tip-to-tail diagram and find the vector sum
Note: Just label as positive magnitudes
| Vtotal | = ?
18.0 m/s
14.0 m/s
Vector sum or Vtotal

91. Adding Vectors Using the Component Method
Step Three: Add the x components and y components
Vx (total) = m/s Vy (total) = m/s
Step Four: Draw a tip-to-tail diagram and find the vector sum
Note: Just label as positive magnitudes
| Vtotal | = ( )1/2
18.0 m/s
14.0 m/s
Vector sum or Vtotal

92. Adding Vectors Using the Component Method
Step Three: Add the x components and y components
Vx (total) = m/s Vy (total) = m/s
Step Four: Draw a tip-to-tail diagram and find the vector sum
Note: Just label as positive magnitudes
| Vtotal | = ( )1/2
= 22.8 m/s
18.0 m/s
14.0 m/s
Vector sum or Vtotal

93. Adding Vectors Using the Component Method
Step Three: Add the x components and y components
Vx (total) = m/s Vy (total) = m/s
Step Four: Draw a tip-to-tail diagram and find the vector sum
Note: Just label as positive magnitudes
| Vtotal | = ( )1/2
= 22.8 m/s
Where is the reference angle?
18.0 m/s
14.0 m/s
Vector sum or Vtotal

94. Adding Vectors Using the Component Method
Step Three: Add the x components and y components
Vx (total) = m/s Vy (total) = m/s
Step Four: Draw a tip-to-tail diagram and find the vector sum
Note: Just label as positive magnitudes
| Vtotal | = ( )1/2
= 22.8 m/s
Where is the reference angle?
18.0 m/s Θ
14.0 m/s
Vector sum or Vtotal

95. Adding Vectors Using the Component Method
Step Three: Add the x components and y components
Vx (total) = m/s Vy (total) = m/s
Step Four: Draw a tip-to-tail diagram and find the vector sum
Note: Just label as positive magnitudes
| Vtotal | = ( )1/2
= 22.8 m/s
Θ = ?
18.0 m/s Θ
14.0 m/s
Vector sum or Vtotal

96. Adding Vectors Using the Component Method
Step Three: Add the x components and y components
Vx (total) = m/s Vy (total) = m/s
Step Four: Draw a tip-to-tail diagram and find the vector sum
Note: Just label as positive magnitudes
| Vtotal | = ( )1/2
= 22.8 m/s
Θ = Tan-1 ( 14.0/18.0 ) don't sub negatives
18.0 m/s Θ
14.0 m/s
Vector sum or Vtotal

97. Adding Vectors Using the Component Method
Step Three: Add the x components and y components
Vx (total) = m/s Vy (total) = m/s
Step Four: Draw a tip-to-tail diagram and find the vector sum
Note: Just label as positive magnitudes
| Vtotal | = ( )1/2
= 22.8 m/s
Θ = Tan-1 ( 14.0/18.0 ) don't sub negatives
= 37.9°
18.0 m/s Θ
14.0 m/s
Vector sum or Vtotal

98. Adding Vectors Using the Component Method
Step Three: Add the x components and y components
Vx (total) = m/s Vy (total) = m/s
Step Four: Draw a tip-to-tail diagram and find the vector sum
Note: Just label as positive magnitudes
| Vtotal | = ( )1/2
= 22.8 m/s
Θ = Tan-1 ( 14.0/18.0 ) don't sub negatives
= 37.9°
Vtotal = ?
18.0 m/s Θ
14.0 m/s
Vector sum or Vtotal

99. Adding Vectors Using the Component Method
Step Three: Add the x components and y components
Vx (total) = m/s Vy (total) = m/s
Step Four: Draw a tip-to-tail diagram and find the vector sum
Note: Just label as positive magnitudes
| Vtotal | = ( )1/2
= 22.8 m/s
Θ = Tan-1 ( 14.0/18.0 ) don't sub negatives
= 37.9°
Vtotal = 22.8 m/s [ W37.9°S] or [S52.1°W]
18.0 m/s Θ
14.0 m/s
Vector sum or Vtotal

100. Try this: Add these vectors using the component method: 12. 0 m [E25
Try this: Add these vectors using the component method: m [E25.0° S] m [N38.0°W] m [S]

101. Try this: Add these vectors using the component method: 12. 0 m [E25
Try this: Add these vectors using the component method: m [E25.0° S] m [N38.0°W] m [S] A
A = HcosΘ O = HsinΘ
= 12.0cos25.0° = 12.0 sin 38.0°
= = 5.07
Δdx = m Δdy = m
A = HcosΘ O = HsinΘ
= 14cos38° = 14sin38°
= = 8.62
Δdx = m Δdy = m
Chart Δdx (total) = m m + 0 m = 2.3 m
Δdy (total) = m m m = -5.1 m
25.0° O
H = 12 O
H = 14 A
38.0°

102. Try this: Add these vectors using the component method: 12. 0 m [E25
Try this: Add these vectors using the component method: m [E25.0° S] m [N38.0°W] m [S]
Chart Δdx (total) = m m + 0 m = 2.3 m
Δdy (total) = m m m = -5.1 m
Tip-to-tail
|Δdtotal | = ( )1/2
= 5.6 m
θ = tan-1(O/A)
= tan-1(5.1/2.3)
= 66°
Δdtotal = 5,6 m [E66°S] or [S24°E]
2.3 Θ
5.1
Δdtotal No
negatives