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11-27-07 - Intro To Vectors


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11-27-07 - Intro To Vectors

  1. 1. VECTORS Chapter 4.1
  2. 2. Scalar or Vector? <ul><li>What am I, a scalar or vector quantity? </li></ul><ul><ul><li>Scalar – only magnitude </li></ul></ul><ul><ul><li>Vector – magnitude AND direction </li></ul></ul><ul><ul><ul><li>Velocity, Force, Acceleration, Displacement </li></ul></ul></ul><ul><li>5 mph </li></ul><ul><li>5 mph north </li></ul><ul><li>15 m/s northwest </li></ul><ul><li>1.2 N west </li></ul><ul><li>10 m/s </li></ul>
  3. 3. Vectors Vectors have magnitude and direction. They add or subtract depending on their directions. Parallel vectors are pretty simple: 50 N 50 N = 100 N + 50 N 50 N = + 0 N What if the vectors are NOT parallel: Example: What if I walked 16 km East and 12 km North The result is a NET movement of 20 km Northeast 16 km East 12 km North 20 km Northeast Component Vectors Resultant Vector
  4. 4. <ul><li>To work with vectors, it is important to know how to perform vector addition both graphically and analytically. </li></ul><ul><ul><li>Graphically – draw vectors to scale and measure </li></ul></ul><ul><ul><li>Analytically – use formulas </li></ul></ul>
  5. 5. <ul><li>When 2 or more vectors act on an object, they act independently of one another. </li></ul><ul><li>Their combined action will result in a net effect. </li></ul>
  6. 6. <ul><li>The purpose of vector addition is to determine the net figure and direction. </li></ul><ul><li>The net figure is called the “resultant.” </li></ul>
  7. 7. <ul><li>The best way to determine the measurement of a resultant is mathematically, but sometimes it is necessary to draw the vectors to scale and measure the resultant with a ruler and protractor. </li></ul>
  8. 8. Let’s look at an example… <ul><li>Let’s examine a picture of a boat crossing a river. </li></ul><ul><li>The boat is moving due east at 8.0 m/s, and the river is flowing due south at 5.0 m/s. </li></ul><ul><li>Find your resultant and direction </li></ul>