1. Vectors

2. Scalars and Vectors Scalar – has only magnitude (or size)
Vector – has both magnitude and direction
Examples of Scalars:
Mass
Distance
Time
Density
Work
Energy
Examples of Vectors:
Displacement
Velocity
Acceleration
Force
Momentum
Angular momentum

3. Scalars and Vectors
Which are scalars? Which are vectors?

5. Vector Addition - One Dimension
Always add vectors “tip-to-tail”
Resultant is the sum of the first two vectors

6. When adding vectors together, the answer is called “The Resultant”.

7. Vector Addition – One Dimension
Always add vectors “tip-to-tail”
Place the tip of the first vector next to the tail of the second
“Resultant” is the sum of the first two vectors

8. Vector Addition – Two Dimensions
Still add vectors “tip-to-tail”
Resultant has both magnitude (the numerical sum of the first two vectors) and direction (typically an angle or direction – north, south, etc.)
Example: A hiker travels 4 miles east
Which is the magnitude?
Which is the direction?
Is this a vector?

9. Vector Addition – Hiker Example
Example: A hiker travels 8 miles east then 2 miles north. How far is he from where he started? At what angle?
Draw the resultant.
Use pythagorean theorem to calculate distance.
Use geometry (SOH-CAH-TOA) to calculate angle.
2 mi
8 mi

10. SOH-CAH-TOA
SOH:
CAH:
TOA: R x y θ

11. Vector Addition
You are in a plane flying east at 45 km/hr when you hit a crosswind moving north at 25 km/hr. What is your resultant velocity? +
25 km/hr north
45 km/hr east
V=?
25 km/hr north
=?
45 km/hr east

12. V=?
Vy = 25 km/hr
=?
Vx = 45 km/hr
 = north of east

13. Resolving Vectors into components

14. Resolving Vectors
Component – the projection of a vector onto a coordinate axis
Vectors are at angles
Want the x-component and y-component
i.e., the x “piece” and the y “piece” of the vector
VECTOR
“Y-component”
“x-component”

15. Resolving Vectors
You travel 30 meters at an angle that is 250 north of east. Resolve this vector into its components
30 m
250

16. 30 m
250

17. Positive or Negative Components?y
X = pos
Y = pos
X = neg
Y = pos x
X = neg
Y = neg
X = pos
Y = neg

18. “Breaking Vectors down into Components” Practice… (& Walking the Vectors Lab, if time)