1. Enduring Understanding: Modeling is widely used to represent physical and kinematic information.
Essential Question: What are the practical applications of modeling physical and kinematic information?

2. Let’s say you draw an arrow. How long is it?
60 cm

3. If we say, 1 cm = 20 miles
Then, the arrow on the last slide represents 1200 miles.
How might this be useful? Example?

6. Vectors are scale model arrow representations.
Vectors have magnitude (size) and direction.
Recall: Magnitude without direction is called a scalar.

7. Scalar Vector
Distance Displacement
Speed Velocity
Time Acceleration

8. Vector Addition
The resultant is one vector that represents the addition of two or more vectors.
What is the resultant displacement if you add 2 m east to 3 m east?

9. Add vectors head to tail
Add vectors head to tail. The arrow is the head, the other end is the tail.
2 m east m east
Resultant 5 m east

10. Head to Tail Vector Addition

12. Draw a head to tail vector diagram showing the addition of 10 m north + 5 m south. What is the resultant displacement?
5 m south
10 m north
Resultant: 5 m north

13. What is the resultant of 3 m east + 4 m north?

14. Use the Pythagorean Theorem to find the magnitude of the resultant.

15. What is the resultant magnitude of 3 m east + 4 m north?
The magnitude = 5 m
4 m
3 m

16. To find direction:
Find the angle of the resultant and name the direction. Find the angle closest to the starting point (where 2 tails meet). Use inverse tangent
θ = tan-1 (4/3)
= 53.1°
4 m θ
3 m

17. For direction, it’s always the 2nd direction ‘of’ the 1st direction.
In this case, the 1st direction traveled is
East, the 2nd direction is North.
Therefore the direction is N of E.
The resultant is:
53.1° N of E
4 m θ
3 m

19. Example for adding more than 2 vectors together:

20. A boat heads west across a 300 m wide river at 10 m/s
A boat heads west across a 300 m wide river at 10 m/s. The current pushes the boat south at 5 m/s. What is the resultant speed of the boat?
° S of W
How long does it take to cross the river?
30s
How far downstream does the boat travel?
150 m