unit 2 two dimensional motion and vectors. if two vectors are given such that a + b = 0, what can...
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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.
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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
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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.
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Sample Problem
11
Equal Vectors
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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
19
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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END