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KD1 Vectors
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Scalar vs. VectorScalar-Quantity having magnitude only (no
direction)Ex: Temp., mass, time, speed
Vector-Quantity having magnitude AND directionEx: Force, displacement, velocity, acceleration
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Examples: Scalar or Vector?1) 15 m/s up2) 21 degrees F3) 100 watts4) 50 km N of
W5) 75 mi/hr
1)Vector2)Scalar3)Scalar4)Vector5)Scalar
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3 Ways to Represent Vectors1. Symbols:2. Words: 250 m/s East3. Arrows drawn to scale
Need: a) direction indicator b) scale: 1 cm=50 m/s c) directional arrow drawn proper
length
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Example:Represent 250 m/s E
: a) direction indicator b) scale: 1 cm= 50 m/s c) directional arrow drawn proper
length
5 cm 5 (50 m/s)=250 m/s E
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VectorsLength of arrow=magnitudeHead of arrow=direction
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VectorsComponents-Vectors whose sum is the
resultantcan be simplified into horizontal (X) and vertical (Y) vectors
Resultant-The vector sum of 2 or more components
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2 Ways of Finding the Resultant Vector1. Graphical Method-uses a scale vector
drawingAlways add vectors “tail” to “head”Resultant is drawn from “tail” of 1st to “head” of
last vector
EXAMPLES! R
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Graphical MethodWhen subtracting vectors, change
subtraction to additionA – B = A + (-B)
The negative (-B) changes the direction of the vector
Negative vectors:ADD the OPPOSITE direction of the original
vector
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2 Ways of Finding the Resultant Vector2. Component Method-Uses calculations to
find resultant
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Trig. Review (Right angles)Sin=Cos=Tan=
Pythagorean Theorem
Coordinate System
Opp / HypAdj / HypOpp / Adj
a2 + b2 = c2
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Trig.All vectors can be broken down into
horizontal (x) and vertical (y) components
Example: F=58 N
Fx
Fy30
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ChecksWhich color of the Triangle
represents the hypotenuse?Which color of the Triangle
represents the opposite side?Which color of the Triangle
represents the adjacent side?Which color represents the X
coordinate?Which color represents the Y
coordinate?
Blue
Green
Red
Green
Red
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Distance vs. DisplacementDistance-
Displacement-
How far something move without regards to the direction(example - 3 miles east and 4 miles north is a total distance of 7 miles)
The change in position of something WITH respects to the direction(example - 3 miles east and 4 miles north is a total displacement of 5 miles North East
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Steps to Add Vectors by Component Method1) Break down each vector into x and y
components2) Add similar components
Add all “x” componentsAdd all “y” components
3) Use Pythagorean theorem to find magnitude of resultant
4) Use tangent function to find angle and direction of resultant
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EXAMPLES!
+ =
– =
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ExamplesGiven the scale and the RED arrow, describe
the vector in words (use both magnitude and direction)
1 cm = 5 m/s
Presume the red arrow is 7 cm
Answer = 35 m/s @ 33˚ S of WOR 35 m/s @ 57˚ W of S
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ExamplesCalculate the horizontal (X) and vertical (Y)
components.
The vector is representing 35 m/s @ 33˚ S of W
Sin θ = opp / hyp
Sin 33 = opp / 35
.545 = opp / 35
Opp (Y) = 19 m/s
Cos θ = adj / hyp
Cos 33 = adj / 35
.839 = adj / 35
Adj (X) = 29 m/s