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Vector Basics (click here) Vector Basics You can view this applet if you have Geometers Sketchpad. Source: Mathforum.org Check your learning….. What are the components of a vector?

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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

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Heading starts out from due North clockwise Start out at Due North Due North 0 degrees Clockwise Due East 90 degrees Due South 180 degrees Due West 270 degrees Or 360 degrees after complete rotation

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Direction starts out from East counter-clockwise Start out at East North 90 degrees Counter Clockwise East 0 degrees Or 360 after complete rotation South 270 degrees West 180 degrees START HERE

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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

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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.

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Vector Addition Visual (click here) Vector Addition Visual What kind of shape are you creating when combining 2 vectors? Triangle

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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 Addition red vector = vector a; green vector = vector b; Blue vector = resultant vector (a+b)

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Vector a (not drawn to scale) Horizontal A x component Vertical A y Compone nt 25 A x = r cos 25 = 143 cos 25 = 129.6 A y = r sin 25 = 143 sin 25 = 60.43 r = 143

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r = 110 Horizontal B x 60 B x = r cos 60 = 110 cos 60 = 55 B y = r sin 60 = 110 sin 60 = 95.26 vertical B y

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horizontal and vertical components of 2 vectors

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Resultant Vector A + B A x + B x = 129.6 + 55 = 184.6 A y + B y = 60.43 + 95.26 = 155.69 184.6 155.69

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Resultant Vector A + B 184.6 155.69 What formula can you use? Pythagorean Theorem = 241.49

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Resultant Vector A + B 184.6 155.69 = 241.49

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