vector addition
DESCRIPTION
Vector Addition. Adding Multiple Vectors by Drawing. To add vectors you place the base of the second vector on the tip of the first vector You make a path out of the arrows like you’re drawing a treasure map - PowerPoint PPT PresentationTRANSCRIPT
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Vector Addition
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Adding Multiple Vectors by Drawing
To add vectors you place the base of the second vector on the tip of the first vector
You make a path out of the arrows like you’re drawing a treasure map
The answer vector (called the resultant) is the vector that connects the start of the path to the end of the path.
Measure the resultant with a ruler to find the magnitude.
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Add These Vectors by Drawing
3 cm @ 90° + 6 cm @ 0° = ?
resultant (answer vector)
![Page 4: Vector Addition](https://reader036.vdocuments.us/reader036/viewer/2022062422/56813554550346895d9cb65e/html5/thumbnails/4.jpg)
Tip-to-Tail
This method of adding vectors is called the “Tip-to-tail method” since you put the tail of the second vector on the tip of the first vector
resultant (answer vector)
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Adding Vectors Mathematically When adding perpendicular vectors
you use the Pythagorean Theorem
a
bc
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Finding the Direction
When adding vectors by drawing you use a protractor and measure the angle of the resultant.
When adding vectors mathematically you use Trigonometry to find the direction of the resultant.
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Trig Functions
Sine (sin) Cosine (cos) Tangent (tan) Each function uses two sides of a
right triangle The angle we are using is labeled with
the Greek letter “theta” or “θ”
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SOH-CAH-TOA
θ
hypotenuse
op
posi
te
adjacent
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Angles
Angles are measured from the +x-axis
Quadrant 1: 0°-90°Quadrant 2: 90°-180°
Quadrant 3: 180°-270° Quadrant 4: 270°-360°
Your calculator will give you the angle
to the closest part of the x-axis. You need to add or subtract to adjust the angle to the ranges shown.
y
x
![Page 10: Vector Addition](https://reader036.vdocuments.us/reader036/viewer/2022062422/56813554550346895d9cb65e/html5/thumbnails/10.jpg)
Example: MagnitudeA hiker hikes 22 km East, then 11 km North. Determine the magnitude and direction of the hiker’s displacement.
θ
22 km
11 kmresultant
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Example: DirectionA hiker hikes 11 km East, then 22 km North. Determine the magnitude and direction of the hiker’s displacement.
θ
22 km
11 kmresultant
Your calculator must be in degrees mode!
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