Vectors - Finding Vector Components

Contents:• Definition of vector components• Whiteboards: Writing the notation• How to find components• Whiteboard Am to VC

Vectors - What components are

TOC

A:

X - Component

Y - Component

Vectors - What components are

TOC

Suppose A = 5 cm

Ax = 4 cm

Ay = 3 cm

A = 4 cm x + 3 cm y(This is how you write it)

^ ^

Whiteboards: Writing the notation

1 | 2 | 3

4.5 m x + 3.2 m y

4.5 m

3.2 m

-1.2 m x + -3.9 m y

1.2 m

3.9 m

-1.9 m x + 4.1 m y

1.9 m

4.1 m

Whiteboards: Drawing the components

1 | 2 | 3 | 4 | 5 | 6

Draw the components from the tail to the tip using arrows

32o

38o

Draw the components from the tail to the tip using arrows

13o

Draw the components from the tail to the tip using arrows

22o

Draw the components from the tail to the tip using arrows

26o

Draw the components from the tail to the tip using arrows

42o

Draw the components from the tail to the tip using arrows

Vectors - Try this yourself

Get out your calculatortype:sin 90 <ENTER>1????If not <2nd?> MODECursor arrows to “Degree”<ENTER> <CLEAR>Try again (sin 90)

Vectors - Finding Components - step by step

Step 1: Draw the componentsUse Arrows/Around angleFrom tail to tip of vector

Step 2: Find the Adj and Opp sides:A = (Hyp)Cos()O = (Hyp)Sin()

Step 3: Write as components:Decide x and yDecide + and –Write as ______ m x + ______ m y

12 m

27o

Step 1: Draw the componentsUse Arrows/Around angleFrom tail to tip of vector

Step 2: Find the Adj and Opp sides:A = (Hyp)Cos()O = (Hyp)Sin()

Step 3: Write as components:Decide x and yDecide + and –Write as ______ m x + ______ m y

8.0 m

Vectors - Try this yourself

23.0 m/s31.0o

1. Draw the Components2. Figure the components with sin and cos3. Write the answer in VC Notation

-11.8 m/s x + 19.7 m/s y

= 90 + 31 = 121o

23cos(121) x + 23sin(121) y-11.846 x + 19.715 y

Whiteboards: AM to VC

1 | 2 | 3 | 4 | 5

22.8 km x + 14.4 km y

32.2o

27.0 km

= 32.2o

27.0cos(32.2) x + 27.0sin(32.2) y22.84721549 14.3876594522.8 km x + 14.4 km y

-4.9 ft x + 1.1 ft y

5.0 feet77o

-5sin(77) x + 5cos(77) y-4.871850324 1.124755272-4.9 ft x + 1.1 ft y

37 m x + -19 m y

42 m

27o

+42cos(27) x + -42cos(27) y37.42227402 -19.0676009937 m x + -19 m y

68 N x + -87 N y

110.0 N38o

+110.0sin(38) x + -110.0cos(38) y67.72276229 -86.681182968 N x + -87 N y

-4.3 m/s x + -2.5 m/s y

5.0 m/s

30.0o

-5.0cos(30) x + -5.0sin(30) y-4.330127019 -2.5-4.3 m/s x + -2.5 m/s y