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  # Applied 40S April 29, 2009
  
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  ### Applied 40S April 29, 2009
  
  1. 1. Vector Addition many directions where to go by ﬂickr user regolare
  2. 2. The Tools of the Trade: Some Trigonometric Equations ... The Pythagorean Theorem The Sine Law A A c b c B C b a C a B SAS The Cosine Law SSS A c b B C a
  3. 3. Some Useful Properties of Angles ... Opposite Angles When two lines intersect, the angles opposite each other at the point of intersection are a° congruent. b° b° a° Mnemonic: X Alternate Angles Angles on alternate sides of a transversal are congruent. a° b° Mnemonic: Z b° a° Corresponding Angles Angles on coresponding sides of a transversal are congruent. b° a° Mnemonic: F b° a°
  4. 4. TRANSVERSAL TRANSVERSAL
  5. 5. ABCD is a parallelogram with AD = DE. Each segment in the diagram is a vector. Answer the following questions. HOMEWORK (a) Name a vector (b) Name a vector that that is equal to AD is the opposite of AB (d) Name a vector that is parallel (c) Name a vector that to but not equal to EA or EB is collinear with BA
  6. 6. State the magnitude and direction of each vector. HOMEWORK
  7. 7. HOMEWORK State the magnitude and direction of each vector. (You can determine the answer using ruler and protractor.)
  8. 8. Draw scale diagrams of the following vectors using pencil, ruler, protractor, and paper. Label the diagram. Be sure to indicate the scale you used. HOMEWORK (a) Tiffany walks 13 blocks in a direction E15°S. (b) A boat is headed 300° at 45 km/h.
  9. 9. Adding Vectors Using Scale Diagrams ... A vector is represented by an arrow. It's LENGTH determines it MAGNITUDE and the TIP determines its DIRECTION. When a vector is moved around in a plane it is considered to be the same vector. These two vectors are TAIL considered to be identical: Vectors can be added an any order. TIP When two vectors are added a new vector is made. It is called the RESULTANT vector. → a means quot;vector aquot; a means quot;magnitude of vector aquot; There are two techniques that we use to add vectors using a scale diagram ...
  10. 10. A ball is thrown horizontally against a wall with a velocity of 10 m/s. It rebounds with a velocity that has a magnitude of 75% of the initial velocity. Visualizing the Process ... Sketch two vectors to represent the two velocities. > l ai -t The Triangle Method -to > p ti Resultant of Forces (Addition of Vectors) http://www.walter-fendt.de/ph14e/resultant.htm
  11. 11. The Triangle Method ... HOMEWORK We use the triangle method when the vectors are arranged tip-to-tail. 6cm Scale: 1 cm = 2 km 10cm RESULTANT 23.4 km 59° S of E RESULTANT 11.7 cm 59° S of E Remember, we use measurements with a ruler and protractor to ﬁnd the quot;answers.quot;
  12. 12. You try ... HOMEWORK Add each pair of vectors using the triangle method. Find Find is 3 meters east is 3 meters southwest is 4 meters north is 4 meters west
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