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