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Vectors - Finding Vector Components
Contents:• Definition of vector components• Whiteboards: Writing the notation• How to find components• Whiteboard Am to VC
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Vectors - What components are
TOC
A:
X - Component
Y - Component
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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)
^ ^
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Whiteboards: Writing the notation
1 | 2 | 3
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4.5 m x + 3.2 m y
4.5 m
3.2 m
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-1.2 m x + -3.9 m y
1.2 m
3.9 m
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-1.9 m x + 4.1 m y
1.9 m
4.1 m
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Whiteboards: Drawing the components
1 | 2 | 3 | 4 | 5 | 6
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Draw the components from the tail to the tip using arrows
32o
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38o
Draw the components from the tail to the tip using arrows
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13o
Draw the components from the tail to the tip using arrows
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22o
Draw the components from the tail to the tip using arrows
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26o
Draw the components from the tail to the tip using arrows
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42o
Draw the components from the tail to the tip using arrows
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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)
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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
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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
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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
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Whiteboards: AM to VC
1 | 2 | 3 | 4 | 5
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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
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-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
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37 m x + -19 m y
42 m
27o
+42cos(27) x + -42cos(27) y37.42227402 -19.0676009937 m x + -19 m y
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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
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-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