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the Vectors

the Vectors. Vectors and Scalars. Vectors: a) have both magnitude and direction (Ex) Driving to Palm Spring at 70 mph (=velocity) b) shown as arrows: The head points to the direction and the length is the magnitude c) named with a letter with an arrow written above (Ex) 2) Scalars:

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the Vectors

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  1. the Vectors

  2. Vectors and Scalars • Vectors: a) have both magnitude and direction (Ex) Driving to Palm Spring at 70 mph (=velocity) b) shown as arrows: The head points to the direction and the length is the magnitude c) named with a letter with an arrow written above (Ex) 2) Scalars: a) have only magnitude (Ex) Driving at 70 mph (=speed) b) shown as line segments c) Name as an absolute value (Ex)

  3. Working with Vectors • Parallel vectors have the same direction. (Ex)

  4. 2) Vectors can be moved without being changed as long as the direction and the length remain unchanged (Ex)

  5. 3) The vectors moving in opposition direction (180 ˚ turn-around) have a negative sign

  6. 4) Vectors can be added, subtracted, multiplied or divided. a) The resultant vector is the sum of vectors. b) Treat subtraction as adding “the opposite” c) Vectors can be multiplied or divided by a scalar *We don’t multiply or divide vectors here *When an angle is used to indicate the direction of a vector, the angle is measured from the x-axis counterclockwise.

  7. Adding Vectors • The head (tip)-to-tail method (Ex) Find the resultant vector. Adding Vectors Demo

  8. Subtracting Vectors • Change the subtraction to “adding the opposite” (Ex) Find

  9. Multiplying Vector by Scalar • Multiply the magnitude but keep the same direction (Ex) Find (Ex) Find

  10. Examples 1. A roller coaster moves 85 m horizontally, then travels 45 m at an angle of 30.0˚ above the horizontal. What is its displacement from its starting point? Use graphical techniques.

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