1. UNIT 2 Two Dimensional Motion
And Vectors

2. ConcepTest 3.1a Vectors I
1) same magnitude, but can be in any direction
2) same magnitude, but must be in the same direction
3) different magnitudes, but must be in the same direction
4) same magnitude, but must be in opposite directions
5) different magnitudes, but must be in opposite directions
If two vectors are given such that A + B = 0, what can you say about the magnitude and direction of vectors A and B?

3. ConcepTest 3.1a Vectors I
1) same magnitude, but can be in any direction
2) same magnitude, but must be in the same direction
3) different magnitudes, but must be in the same direction
4) same magnitude, but must be in opposite directions
5) different magnitudes, but must be in opposite directions
If two vectors are given such that A + B = 0, what can you say about the magnitude and direction of vectors A and B?
The magnitudes must be the same, but one vector must be pointing in the opposite direction of the other, in order for the sum to come out to zero. You can prove this with the tip-to-tail method.

4. Monday September 19th
Introduction of Vectors

5. TODAY’S AGENDA UPCOMING… Intro to Vectors
Monday, September 19
Intro to Vectors
Mini-Lesson: Properties of Vectors
Hw: Worksheet Pg
UPCOMING…
Tues: Vector Operations
Wed: More Vector Operations
Thurs: Problem Quiz 1 Vectors
Mini-Lesson: Projectile Motion

6. Notating Vectors This is how you notate a vector… This is how
Text books usually write vector names in bold.
This is how
you notate a vector…
You would write the vector name with an arrow on top.
This is how
you draw a vector…

7. Vector Angle Ranges Quadrant II Quadrant I x Quadrant III Quadrant IVy
Quadrant II
90˚< θ < 180˚
Quadrant I
0˚< θ < 90˚ θ θ x θ θ
Quadrant III
180˚< θ < 270˚
Quadrant IV
270˚< θ < 360˚

8. Direction of Vectors x θ θ What angle range would this vector have?
What would be the exact angle and how would you determine it?
Between 180˚ and 270˚ θ x θ
Between -270˚ and -180˚

9. Magnitude of Vectors
The best way to determine the magnitude of a vector is to measure its length.
The length of the vector is proportional to the magnitude (or size) of the quantity it represents.

10. Sample Problem

11. Equal Vectors

12. Inverse Vectors

13. Right Triangle Trigonometry

14. Hypotenuse2 = Opposite side2 + Adjacent side2
Pythagorean Theorem
Hypotenuse2 = Opposite side2 + Adjacent side2

15. Basic Trigonometric Functions

16. Trigonometric Inverse Functions

17. Trigonometry Refresher:x q
To find the resultant,
To find the angle, q

18. Sample Problem
Tree
tan 50˚ = width/100 m
width = (100 m) tan 50˚
119 m
155 m
width = 119 m
R2 = (119 m)2 + (100 m)2
50˚
100 m
R = 155 m

19. Sample Problem
You are standing at the very top of a tower and notice that in order to see a manhole cover on the ground 50.0 meters from the base of the tower, you must look down at an angle 75.0˚ below the horizontal.
If you are 1.80 m tall, how high is the tower?
tan 75.0˚= height(eye) / 50.0 m
75˚
height(eye) = (50.0 m) tan 75.0˚
height(eye) = 187 m
height(building) = 187 m – 1.80 m
75˚
height(building) = 185 m
50 m

20. END