UNIT 2 – VECTORSSINGLE AND COMBINING VECTORS

(DOES NOT INCLUDE COURSE CORRECTION PROBLEMS)

COURSE 4

What is a vector?

Vector Basics (click here)You can view this applet if you have

Geometer’s Sketchpad. Source: Mathforum.org

Check your learning…..What are the components of a vector?

Vector Components

Magnitude (r) – length (measured in any units of length)

Heading – measured in degrees from due north clockwise

Direction- Measured in degrees from due east

counterclockwise

Since you will be measuring angles with a protractor, use this link to refresh your skills

Using a Protractor to Measure Angles

θ

θ

More about Heading…

Heading starts out from due North clockwise

Start out at Due NorthDue North 0 degrees Clockwise

Due East 90 degrees

Due South 180 degrees

Due West 270 degrees

Or 360 degrees aftercomplete rotation

More about Direction…

Direction starts out from East counter-clockwise

Start out at EastNorth 90 degrees Counter Clockwise

East 0 degreesOr 360 after completerotation

South 270 degrees

West 180 degrees START HERE

Practice Sketching Vectors

Sketch the vectors with the following magnitude and direction

r = 143 ; = 25

r = 110 ; = 60

Check your measurements of the angles against the following link (Skip Intro):

Make and Measure

θ

θ o

o

a→

b→

Vector Components

What kind of shapes can you create by drawing a horizontal and vertical line connecting the vectors’ tail and head? Right Triangles

Connect the 2 vectors tail to head. Make right triangles from the single vectors you drew in the previous slide.

a→+ b

→

Combining Vectors

Vector Addition Visual (click here)

What kind of shape are you creating when combining 2 vectors?

Triangle

Combine the Vectors

Go to following applet to see the resultant vector. You will have to sketch the vectors according to polar coordinates and degrees. The blue vector is your resultant vector. Show components after you connect the vectors to see their components.

Vector Additionred vector = vector a; green vector =

vector b;Blue vector = resultant vector (a+b)

Vector Components cont’d..

Vector ‘a’ (not drawn to scale)

Horizontal Ax component

Vertical Ay Component

25

Ax = r cos 25 = 143 cos 25 = 129.6

Ay = r sin 25 = 143 sin 25 = 60.43

r = 143

Second Vector Components

r = 110

HorizontalBx

60

Bx = r cos 60 = 110 cos 60 = 55

By = r sin 60 = 110 sin 60 = 95.26

verticalBy

Let’s use Trig to find resultant Vector

horizontal and vertical components of 2 vectors

ax +bx =horizontalay +by =vertical

Second Vector Components

Resultant VectorA + B

Ax + Bx = 129.6 + 55 = 184.6

Ay + By = 60.43 + 95.26 = 155.69

184.6

155.69

Resultant Vector Magnitude

Resultant VectorA + B

184.6

155.69

What formula can you use?

Pythagorean Theorem

184.62 +155.692

= 241.49

= 241.49

Resultant Vector Direction

Resultant VectorA + B

184.6

155.69

= 241.49

Direction =tan−1(

155.69184.6

) =40o

40o