Chapter 3 Two Dimensional Motion and Vectors
3.1
Introduction to Vectors
Scalars and Vectors
Scalar (italics in your textbook)
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Vector (boldface in your textbook)
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Vectors are represented by arrows
Vectors can be added graphically (using a protractor. Vectors must have same units)
Tail-to-tip method
Add A + B
Let A = 9 meters east (E) and let B = 4 meters north (N)
Scale: 1 block = 1 meter (1 block = ¼ inch)
Resultant
 The answer obtained from adding vectors
Parallelogram method
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(all vectors are placed tail-to-tail from a common origin)
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Vectors can be added in any order
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Vector subtraction is simply adding the opposite
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Let A = 9 m east (E) and let B = 4 m north (N).
What is the resultant of A – B?
What is the resultant of B – A?
Multiplying a vector by a scalar results in a vector
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Practice problem: Add the following vectors graphically: 11 m E, 5 m S, 6 m W, 2 m N
How could the parallelogram method be used?
H.W. S.R. page 85, #1-13 page 108
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3.2
Vector Operations
The Pythagorean Theorem can be used to find the resultant of any right triangle
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c
a
ө
b
Tom travels 10 km north and 20 km east. What is his displacement?
scale: 1 square = 2.0 km
Tom travels 15 km east, 20 km north, 5 km south, and 7 km west. What is his displacement?
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Practice A page 89
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Practice B page 92
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Resolving Vectors into Components
SOH CAH TOA
c
a
ө
sin ө = opp / hyp
cos ө = adj / hyp
tan ө = opp / adj
b
Consider the hypotenuse “c” to be a vector. Then side “a” and side “b” of the right triangle are called the
“components” of the vector. If we look at right triangles as being part of the Cartesian coordinate system, then:
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Sample problem B page 91
Practice B
1)
The airplane’s motion is a vector with an x-component and a y-component. The truck’s motion has an
x-component only.
2)
3)
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4)
Adding Vectors That Are Not Perpendicular
The strategy for these types of problems is:
1)
Place the vectors on a Cartesian coordinate system, either tip-to-tip, tail-to-tip, or tail from common
origin (depends on the problem and/or method you choose). Label each vector.
2)
Resolve each vector into x and y-components
3)
Add each x component to obtain a single x-component (resultant of all x-components)
4)
Add each y-component to obtain a single y-component (resultant of all y-components)
5)
Make a new Cartesian coordinate system, placing the new x resultant and y resultant on it
6)
Use the Pythagorean Theorem to find the resultant of the x and y components
7)
Use trig functions to find the angle
8)
Report your answer giving magnitude and direction
Sample problem C page 93
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Practice C
Finish Practice C on separate graph paper
HW: page 94 Section Review, page 109 #14 through #26
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