Post on 03-Jan-2016
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VectorsVectorsVectorsVectors
What is a vector quantity?
Vectors
Vectors are quantities that possess magnitude and direction.
»Force»Velocity»Acceleration
What are scalar quantities?
Scalars• Scalars are quantities that possess
only magnitude.• How much money you have• How old you are• How tall you are• Temperature• Pounds• Speed• Length
Represent the following vectors
• A wind velocity of 20 mph due north• A boat traveling 4 knots per hour
heading east• A car traveling 60 mph heading south
Equal Vectors
• Same length• Same direction
Parallel Vectors
Adding VectorsAdding VectorsAdding VectorsAdding Vectors
Three Methods forAdding Vectors
• Tail to Head Method• Parallelogram Method• Component Method
Tail to Head Method
Adding Vectors Tail to Head
Draw Vector A with the correct length and angle.
Draw Vector B with the correct length and angle, but such the Vector B’s tail starts at the head of vector A.
The Vector C is then represented by an arrow from the tail of Vector A to the head of Vector B.
Adding Vectors Same direction
•
Adding VectorsOpposite directions
Adding Vectors
Components
Parallelogram Method
Parallelogram Method
Vector 1
Vector 2
Resulta
nt Vecto
r
Component Method
Component MethodFind the sum of Vector 1 and Vector
2.
Vector 1 is 25 m 50 N of E
Vector 2 is 10 m 45 N of W
Component Method• Using Trigonometry, find the x-
component and the y-component for each vector.
• Add up the x-components.• Add up the y-components.• Use the Pythagorean Theorem and the
trig functions to get the size and direction of the resultant vector.
Finding the x-component
cosadjacent
hypotenuse
X-component
Y-component
Resulta
nt vecto
r
Finding the x-component
Vector 1 is 25 m 50 N of E
X-component
Y-component
50
25 meters
cosadjacent
hypotenuse
ocos 5025 meters
x component
X-component = 25 * cos 50
X- component (vector 1) = 16.1 m
Finding the y-component
sinopposite
hypotenuse
X-component
Y-component
Resulta
nt vecto
r
Finding the y-component
Vector 1 is 25 m 50 N of E
X-component
Y-component
50
25 meters
y-component = 25 * sin 50
y- component (vector 1) = 19.2 m
osin 5025 meters
y component
Finding the x-component
Vector 2 is 10 m 45 N of W
X-component
Y-component
45
10 meterscos
adjacent
hypotenuse
ocos 4510 meters
x component
X-component = 10 * cos 135
X- component (vector 2) = -7.1 m
Finding the y-component
Vector 2 is 10 m 45 N of W
X-component
Y-component
45
10 meterssin
opposite
hypotenuse
osin 4510 meters
y component
y-component = 10 * sin 135
y- component (vector 2) = 7.1 m
Adding the x- components
Vector 1 + Vector 2
16.1 m+ -7.1 m = 9 m
Adding the y-components
Vector 1 + Vector 2
19.2 m+ 7.1 m = 26.3 m
Using the Pythagorean Theorem
c²= a²+ b²c²= 9²+26.3²c²= 772.69
c = 27.8 meters
tanopposite
adjacent
26.3tan
9
1 26.3tan
9
= 71.1 N of E
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Vectors on the GoVectors on the GoVectors on the GoVectors on the Go
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