UNIT 2 Two Dimensional Motion And Vectors. If two vectors are given such that A + B = 0, what can you say about the magnitude and direction of vectors.

UNIT 2Two Dimensional Motion

And Vectors

If two vectors are given

such that A + B = 0, what

can you say about the

magnitude and direction

of vectors A and B?

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

ConcepTest 3.1a Vectors I

If two vectors are given

such that A + B = 0, what

can you say about the

magnitude and direction

of vectors A and B?

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

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.

ConcepTest 3.1a Vectors I

Monday September 19th

4

Introduction of Vectors

TODAY’S AGENDA

Intro to VectorsMini-Lesson: Properties of VectorsHw: Worksheet Pg. 13-14

UPCOMING…

Tues: Vector OperationsWed: More Vector OperationsThurs: Problem Quiz 1 Vectors

Mini-Lesson: Projectile Motion

Monday, September 19

Notating Vectors

6

This is how you notate a vector…

This is how you draw a vector…

Text books usually write vector names in bold.

You would write the vector name with an arrow on top.

7

Vector Angle Ranges

θ

θ

θ

θ

y

x

Quadrant I 0˚< θ < 90˚

Quadrant II 90˚< θ < 180˚

Quadrant III 180˚< θ < 270˚

Quadrant IV 270˚< θ < 360˚

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Direction of Vectors

What angle range would this vector have?What would be the exact angle and how would you determine it?

x

Between 180˚ and 270˚

Between -270˚ and -180˚

θ

θ

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

Pythagorean Theorem

Hypotenuse2 = Opposite side2 + Adjacent side2

15

Basic Trigonometric Functions

16

Trigonometric Inverse Functions

Trigonometry Refresher:

y

xq

To find the resultant,

To find the angle, q

18

Sample Problem

100 m

50˚

tan 50˚ = width/100 mwidth = (100 m) tan 50˚width = 119 m

Tree

119 m

R2 = (119 m)2 + (100 m)2

R = 155 m

155 m

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Sample Problem

50 m

75˚

75˚

tan 75.0˚= height(eye) / 50.0 mheight(eye) = (50.0 m) tan 75.0˚height(eye) = 187 m

height(building) = 187 m – 1.80 mheight(building) = 185 m

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?

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