1. Vectors

2. A vector is a quantity that has both magnitude and direction.
The length of the arrow is proportional to the magnitude of the vector.
30°
20 m/s

3. Scalar Quantities (magnitude only)
Vector Quantities (magnitude and direction)
Speed
Length
Time
Energy
Volume
Temperature
Velocity
Displacement
Acceleration
Force
Momentum
Electric Field
And a whole lot more!

4. How to specify direction
“30 degrees
above the horizontal”
“45 degrees
below the horizontal”
30°
45°

5. How else to specify direction
“30 degrees East of North”
“60 degrees South of West”
30°
60°

6. 20° West of North
45° South of East
70° North of East
10° South of West

7. Vector Addition: Graphical Method
Add vectors tip to tail
When adding vectors, we can move them but not change their magnitude/direction.

8. Vector Addition with Multiple Vectors

9. Add the following vectors:
A. 3 cm West and 4 cm South
B. 5 cm at 45° North of East and cm North

10. Vector Treasure Hunt!

12. Resultants and Components
Components: show how much of the vector is in the x-direction and how much is in the y-direction.
Resultant: A vector that is the sum of two or more vectors.
Resultant vector
x component
y component

13. Calculating Components
bsinθ b θ
acosθ
bcosθ a θ
asinθ

14. Vector Treasure Hunt: Component Form+ _ + _

15. x-components
y-components

16. x-components
y-components

17. Step
x-component
y-component d
-56.3 m
-32.5 m a
-40 m
0 m e
+19.4 m
+72.4 m c
-28.3 m
+28.3 m b
-30 m

18. x-components
y-components

19. Vectors Can Be Added in Any Order

21. Is there an easier way to do this?
Wait a second…
Is there an easier way to do this?

22. Adding Vectors Mathematically
Step
x-component
y-component A
-30 m
0 m B
-40 m C
-28.3 m
28.3 m D
-41 m
-28.7 m E
-32.1 m
38.3 m
Total Total
x-component: y-component:

23. x-component
y-component
resultant

24. There are two ways to add vectors
There are two ways to add vectors. In your treasure hunt activity, you used both ways:
Graphical Method (Step 1)
Mathematical Method(Step 2 and 4)
For each method, describe how the process works. Then use the process to add the two vectors below.

25. Vector Addition: Mathematical
Break vectors down into x and y components. Check the sign of each component.
Add up all of the x-components to determine the x-component of the resultant vector.
Add up all of the y-components to determine the y-component of the resultant vector.
Use the Pythagorean Theorem and inverse trig functions to solve for the magnitude and direction of the resultant vector.

26. Show all of your work in an organized manner.WB
Calculate the net force (magnitude and direction) exerted on the object represented by the force diagram.
30°
12 N
60°
8 N
Show all of your work in an organized manner.