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Vectors and Scalars

Vectors and Scalars. Adding and Subtracting. Pythagorean Theorem. a 2 + b 2 = c 2 10 8 6 4 3

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Vectors and Scalars

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  1. Vectors and Scalars Adding and Subtracting

  2. Pythagorean Theorem • a2 + b2 = c2 10 8 6 4 3 6

  3. Vector vs. Scalar • Scalar: A quantity that has magnitude and no direction. • Vector: A quantity that has magnitude and Direction.

  4. Vectors • Vectors are represented by “vector arrows”, the length of the arrow represents the magnitude and the direction is that of the vector. 2.5m/s East 1m/s North

  5. Adding and Subtracting Scalars • 15Gallons + 3Gallons = ? • 18Gallons • 3Feet – 1.5Feet = ? • 1.5Feet

  6. Adding and Subtracting Vectors • Must have the same units! • Resultant: A vector that represents the sum of two or more Vectors.

  7. Adding Vectors Graphically • When adding two vectors draw the Vectors in the x direction first. • After drawing a Vector the next Vector must be drawn from the tip of the one before it so that its tail is touching it. • (TIP TO TAIL) • Draw a Line from the start to the finish, that is your resultant, Measure it and find the direction using a protractor.

  8. Add the Vectors Graphically • 2m East, 2m East, 3m North • Remember Magnitude and Direction.

  9. Adding Vectors Algebraically • 1. Find x and y components of all vectors • 2. Place components into the appropriate column • 3. Add each column • 4. Subtract North – South / East – West • 5. Draw x Resultant then Tip to Tail y Resultant • 6. Find the magnitude of the resultant • 7. Find the direction of the resultant.

  10. Question • Following directions on a map, a pirate walks 45.0m north then turns and walks 7.5m east. What is his total displacement?

  11. Answer • 45.62m North of East 46.62m Is the angle bigger or smaller than 45 degrees?

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