1. Vectors & Two-Dimensional Motion

2. Vectors in 2D Vectors are a visual representation of motion
Vectors of 2D motion are added in order to find the RESULTANT vector
In order to add vectors, we use trigonometry

3. Adding & Drawing Vector Diagrams
Vectors are always drawn from tail to tip
Vectors can only touch tail to tip

4. Adding & Drawing Vector Diagrams
A man runs 300m east and 400m south. Draw a vector diagram.

5. Adding Vectors
Sam throws a ball north to James and James throws the ball west to Nathan. What is the displacement of the ball?

6. Use Pythagorean’s Theorem
When adding perpendicular vectors, use Pythagorean’s Theorem.
A man runs 300m east and 400m south. Draw a vector diagram and find the displacement of the man.

7. Direction Direction is measured two ways…
RECTANGULAR CORDINATE SYSTEM:

8. ANGLES ARE ALWAYS WRITTEN OPPOSITE OF ADJACENT!!!
Direction
COMMON CARDINAL SYSTEM:
ANGLES ARE ALWAYS WRITTEN OPPOSITE OF ADJACENT!!!

9. Trigonometry & Direction
To solve for direction, trigonometry is used.

10. Sample Problem (19m @ 28° S of E OR 19m @ 62° E of S)
Find the displacement of 6.0m east and 3.2m south.
28° S of E
OR 62° E of S)

11. Sample Problem (1.3x10²m/s @ 47° N of W OR 1.3x10²m/s @ 43° W of N)
Find the velocity of a plane that flies 90m/s west and then 97m/s north.
47° N of W
OR 43° W of N)

12. Homework
p. 38 #1 (a-h)