1. Vectors What is a vector? Examples of vector quantities include:
Displacement i.e. 10 m North
Velocity i.e. 8 m/s West
Acceleration i.e m/s2 East
Force i.e N South

2. Drawing Vectors Vector quantities are represented with a scaled arrow.
The scaled length represents its magnitude and its arrowhead represents its direction.
If the scale 1 cm = 10 km is used for the arrow above, what is the magnitude and direction of the displacement it represents?

3. Arnold pushes a crate to the right across a frictionless floor with a force of 15 N. Draw a vector on the box below from point P to represent the force. Use the scale 1 cm = 5 N.

4. Arnold pushes a crate to the right across a floor with a force of 20 N
Arnold pushes a crate to the right across a floor with a force of 20 N. The force of friction is 10 N. Draw all the horizontal forces acting on the crate. Use the scale 1 cm = 5 N.

5. Draw a vector of a bird’s straight-line flight at a speed of 25 m/s at 20o west of north.
Scale: 1 cm = 10 m/s

6. Draw a vector representing a nomad walking 1 km at 20o north of west.
Scale: 1 cm = 0.2 km

7. Draw a vector representing a car moving at 100 km/hr at 60o south of east.
Scale: 1 cm = 25 km/hr

8. Draw a vector representing a bicycle moving at 3 m/s 40o east of north.
Scale: 1 cm = 1 m/s

9. Vector Addition (and Subtraction)
Sometimes vectors act concurrently on an object. This means that they act on the same point (thing) at the same time. 
However, concurrent vectors do not always act in the same direction.
The sum of 2, or more, vectors is the combined overall effect of the vectors combined. This is called the resultant.

10. Resultant Displacement
1 cm = 10 m

11. Resultant Velocity
1 cm = 5 m/s

12. Resultant Force
1 cm = 10 N

13. Rules for Adding Vectors
Vectors should be added tail to head. The tail of each subsequent vector should be drawn to the head of the previous vector.
The resultant is found by connecting the tail of the first to the head of the last. (the start to the finish)
The order in which the individual vectors are drawn doesn’t matter. The resultant will come out to be the same.

14. Examples ( 1 cm = 10 N)

15. ( 1 cm = 10 N)

16. ( 1 cm = 10 N)

17. ( 1 cm = 10 N)

18. A boat is moving 5 m/s east in a river
A boat is moving 5 m/s east in a river. The current in the river is 2 m/s north. What is the resultant velocity of the boat?

19. A plane is flying 100 m/s due south
A plane is flying 100 m/s due south. The wind speed is 45o west of south. What is the resultant velocity of the plane?

20. Two movers are pushing on a filing cabinet
Two movers are pushing on a filing cabinet. One mover pushes the cabinet with a force of 100 N due east. The other pushes the cabinet with a force of 150 N 20o south of east. What is the resultant force on the cabinet?

21. Maximums and Minimums
When two vectors are added the value of the resultant (overall effect of all the vectors combined) depends on the direction of each vector.
A boat is moving at a velocity of 10 m/s east in a bay that has no current.
What is the boat’s resultant velocity?

22. What is the boat’s resultant velocity if . . . . . .
The bay had a current of 8 m/s east?
The bay had a velocity of 8 m/s west?

23. The bay had a velocity of 8 m/s south?
The bay had a velocity of 8 m/s 30o west of south?

24. Resultant Velocities for the boat (moving @ 10 m/s east) if the current is . . . . .
8 m/s west
8 m/s south
8 m/s east

25. If two vectors are in the same direction ( o) the resultant is a .
If two vectors are in opposite directions ( o) the resultant is a .
If the angle between two vectors is in between 0o and 180o, (this includes 90o) the resultant is in between the and the . (Not necessarily dead center)

26. Equilibrium
Equilibrium is produced when two, or more, vectors cancel each other out and produce a resultant of zero.
An equilibrant is a vector that will produce equilibrium when added to another vector or vectors.

27. Example A force of 5 N to the left is applied to a box.
Draw a vector that would produce equilibrium.
What is the net force?

28. Find the equilibrant of the two forces shown below

29. A system in equilibrium consists of 3 forces acting on an object
A system in equilibrium consists of 3 forces acting on an object. One force is 7 N east and a second force is 2 N west. What is the magnitude and direction of the third force in the system?

30. A system in equilibrium consists of 3 forces acting on an object
A system in equilibrium consists of 3 forces acting on an object. One force is 4 N north and a second force is 6 N west. Draw the vector that represents the third force in the system.

31. The following picture shows a force acting at point P.
Which pair of concurrent forces below would produce equilibrium when added to the force acting on point P?

32. Which set(s) of three concurrent forces could produce equilibrium? 
5 N, 5 N, 5 N
2 N, 7 N, 12 N
3 N, 4 N, 5 N
9 N, 10 N, 20 N

33. Vector Resolution
Determine three vectors that could have vector “A” as a resultant.

34. A single vector can be resolved into an infinite number of components.

35. Vertical Component
100 N
100 N
25 o
100 N

36. Horizontal Component
100 N
100 N
25 o
100 N

37. Determine the horizontal and vertical components of the vector below

38. A child pulls a wagon with a force of 100 N at an angle of 40o to the horizontal. Determine the vertical force she pulls the wagon with.

39. Alphonse pushes a lawnmower with a force of 50 N at an angle of 55o to the horizontal. Determine the force he pushes the lawnmower forward with.