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Subtracting Vectors A – B = ?

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Example Problem What is 30 m/s north minus 15 m/s east?

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Example Problem What is 30 m/s north minus 15 m/s east? Question: How many vectors are there in this problem?

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Example Problem What is 30 m/s north minus 15 m/s east? Question: How many vectors are there in this problem?

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Words Math What is 30 m/s north minus 15 m/s east?

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Mathematically A – B = ? Words Math

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What is 30 m/s north minus 15 m/s east? Mathematically A – B = ? Words Math The Problem: We only know how to add vectors.

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The Trick: Make it Addition A – B = A + (– B)

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The Trick: Make it Addition A – B = A + (– B) Guess: what is – B?

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Time Out! C This is C

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Time Out! C Point in the direction of – C!

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Time Out! C Point in the direction of – C!

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Time Out! C Point in the direction of – C! - C

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Continue

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The Trick: Make it Addition A – B = A + (– B) - B is B in the opposite direction

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The Trick: Make it Addition A – B = A + (– B) - B is B in the opposite direction

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Graphical Addition of Vectors 1.Make a scale drawing. 2.Move the vectors tip- to-tail. 3.Draw the resultant vector (free tail to free tip). 4.Measure the length of the resultant with a ruler. 5.Measure the direction of the resultant with a protractor. A + (– B) 1 cm = 5 m/s

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Graphical Addition of Vectors 1.Make a scale drawing. 2.Move the vectors tip- to-tail. 3.Draw the resultant vector (free tail to free tip). 4.Measure the length of the resultant with a ruler. 5.Measure the direction of the resultant with a protractor. A + (– B) 1) Which are tip-to-tail? 3) 2) 4)

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Graphical Addition of Vectors 1.Make a scale drawing. 2.Move the vectors tip- to-tail. 3.Draw the resultant vector (free tail to free tip). 4.Measure the length of the resultant with a ruler. 5.Measure the direction of the resultant with a protractor. A + (– B) 1) Which are tip-to-tail? 3) 2) 4)

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Graphical Addition of Vectors 1.Make a scale drawing. 2.Move the vectors tip- to-tail. 3.Draw the resultant vector (free tail to free tip). 4.Measure the length of the resultant with a ruler. 5.Measure the direction of the resultant with a protractor. A + (– B) 1) Draw the resultant for 1): from point ___ to point ___? 2) c b a

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Graphical Addition of Vectors 1.Make a scale drawing. 2.Move the vectors tip- to-tail. 3.Draw the resultant vector (free tail to free tip). 4.Measure the length of the resultant with a ruler. 5.Measure the direction of the resultant with a protractor. A + (– B) 1) Draw the resultant for 1): from point ___ to point ___? 2) c b a ac

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Graphical Addition of Vectors 1.Make a scale drawing. 2.Move the vectors tip- to-tail. 3.Draw the resultant vector (free tail to free tip). 4.Measure the length of the resultant with a ruler. 5.Measure the direction of the resultant with a protractor. A + (– B) 1) Draw the resultant for 2): from point ___ to point ___? 2) f d e

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Graphical Addition of Vectors 1.Make a scale drawing. 2.Move the vectors tip- to-tail. 3.Draw the resultant vector (free tail to free tip). 4.Measure the length of the resultant with a ruler. 5.Measure the direction of the resultant with a protractor. A + (– B) 1) Draw the resultant for 2): from point ___ to point ___? 2) f d e fd

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Graphical Addition of Vectors 1.Make a scale drawing. 2.Move the vectors tip- to-tail. 3.Draw the resultant vector (free tail to free tip). 4.Measure the length of the resultant with a ruler. 5.Measure the direction of the resultant with a protractor. A + (– B) 1) Notice: the resultant is the same for option 1) and option 2). 2)

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Graphical Addition of Vectors 1.Make a scale drawing. 2.Move the vectors tip- to-tail. 3.Draw the resultant vector (free tail to free tip). 4.Measure the length of the resultant with a ruler. 5.Measure the direction of the resultant with a protractor. A + (– B) 1 cm = 5 m/s (6.70)(5) m/s = 33.5 m/s 6.70 cm

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Graphical Addition of Vectors 1.Make a scale drawing. 2.Move the vectors tip- to-tail. 3.Draw the resultant vector (free tail to free tip). 4.Measure the length of the resultant with a ruler. 5.Measure the direction of the resultant with a protractor. A + (– B) 63˚

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Graphical Addition of Vectors 1.Make a scale drawing. 2.Move the vectors tip- to-tail. 3.Draw the resultant vector (free tail to free tip). 4.Measure the length of the resultant with a ruler. 5.Measure the direction of the resultant with a protractor. A + (– B) 33.5 m/s @ 63˚ north of west 1 cm = 5 m/s 63˚ Your final answer!

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Motion Notes (Continued):

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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.

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.

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