Subtracting Vectors AB Example Problem What is 30

Subtracting Vectors A–B=?

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

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

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

Words Math What is 30 m/s north minus 15 m/s east? Mathematically A–B=?

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

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

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

Time Out! C This is C

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

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

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

A + (– B) 1 cm = 5 m/s 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) Which are tip-to-tail? 1) 2) 3) 4) 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) 2) 1) a • • b • c Draw the resultant for 1): from point ___ to point ___? 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) 2) a • • b • c Draw the resultant for 1): c to point ___? a from point ___ 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) Graphical Addition of Vectors 2) d • e • • f Draw the resultant for 2): from point ___ to point ___? 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) Graphical Addition of Vectors 2) d • e • • f Draw the resultant for 2): from point ___ f to point ___? d 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) 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. Notice: the resultant is the same 5. Measure the direction for option 1) and option 2). of the resultant with a protractor. 1) 2)

A + (– B) 1 cm = 5 m/s 6. 70 cm (6. 70)(5) m/s = 33. 5 m/s 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˚ 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 63˚ 33. 5 m/s @ 63˚ north of west Your final answer! 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.

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