Post on 13-Jan-2016
KD1 Vectors
Scalar vs. VectorScalar-Quantity having magnitude only (no
direction)Ex: Temp., mass, time, speed
Vector-Quantity having magnitude AND directionEx: Force, displacement, velocity, acceleration
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
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
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
VectorsLength of arrow=magnitudeHead of arrow=direction
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
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
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
2 Ways of Finding the Resultant Vector2. Component Method-Uses calculations to
find resultant
Trig. Review (Right angles)Sin=Cos=Tan=
Pythagorean Theorem
Coordinate System
Opp / HypAdj / HypOpp / Adj
a2 + b2 = c2
Trig.All vectors can be broken down into
horizontal (x) and vertical (y) components
Example: F=58 N
Fx
Fy30
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
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
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
EXAMPLES!
+ =
– =
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
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