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INTRO TO VECTORS DeKalb County Schools

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INTRO TO VECTORS DeKalb County Schools Powered By Docstoc
					                          GPS

• SP1. Students will analyze the relationships
  between force, mass, gravity, and the motion of
  objects.
  – b. Compare and contrast scalar and vector quantities.
    SCALARS AND VECTORS
• Scalars only have magnitude (ex. 50 m)
• Vectors have magnitude and direction (ex. 50
  m, North)
• When you combine two or more vectors the
  sum is called the resultant.
• For example in 1-D:
  50 m North and 30 m South;
  the resultant is 20 m North (+50 m + (-30 m))
                               VECTOR BASICS




Images:
http://www.physicsclassroom.com/Class/vec
tors/u3l1a.cfm
http://www.physicsclassroom.com/Class/vectors/U3l1b.cfm




                                                               DIMENSION
                                                          THE RESULTANT IN ONE
                                                  DIRECTION




Images:
http://www.physicsclassroom.com/Class/vectors/u
3l1a.cfm
http://www.physicsclassroom.com/mmedia/vectors/vd.cfm
                 THE RESULTANT IN TWO
                  DIMENSIONS (X AND Y)

http://www.physicsclassroom.com/Class/vect
ors/U3l1b.cfm
   PROPERTIES OF VECTORS
• Vectors can be moved parallel to themselves in
  a diagram.
• Vectors can be added in any order. For
  example, A + B is the same as B + A
• To subtract a vector, add its opposite. SIGNS
  (DIRECTION) ARE VERY IMPORTANT!!!
• Multiplying or dividing vectors by scalars
  results in vectors. For example: When you
  divide displacement (x or  y) by time (s) the
  result is velocity (v).
http://www.physicsclassroom.com/mmedia/vectors/ao.cfm
RESULTANTS CAN BE DETERMINE
      GRAPHICALLY OR
      ALGEBRACIALLY
• When determining the resultant graphically you must be
  careful of several factors.
• Your scale must be determined and measured
  accurately with a ruler.
• Your angles (directions) must be done with a protractor.
• ALWAYS DRAW YOUR VECTORS FROM HEAD TO
  TAIL!!!!!       TAIL                  HEAD
• The resultant is always from the head of your last vector
  to the tail of your first vector.
DETERMINING SCALE




   http://www.physicsclassroom.com/Class/vectors/u3l1a.cfm
GRAPHICALLY DETERMINING
      A RESULTANT
       http://www.physicsclassroom.com/Class/vectors/U3l1b.cfm
         DETERMINING
    RESULTANTS BY ALGEBRA
      AND TRIGONOMETRY
• You must use the Pythagorean theorem and
  trigonometry to determine a resultant.
• WE ONLY USE DEGREES IN THIS CLASS!! NO
  RADIANS!!!!
• You must know SOHCAHTOA!!
• You must be able to use your calculator correctly!
• The resultant is always from the head of your last vector
  to the tail of your first vector.
• Direction is always from the tail of the first vector.
http://www.physicsclassroom.com/Class/vectors/U3l1b.cfm
http://www.physicsclassroom.com/Class/vectors/U3l1b.cfm
http://www.physicsclassroom.com/mmedia/vectors/plane.cfm



                                                           REAL LIFE VECTORS
http://www.physicsclassroom.com/Class/vectors/U3l1b.cfm
    ANSWERS TO PRACTICE
• PRACTICE A:
    11.18 km at 26.56 º W of N   OR
    11.18 km at 63.44º N of W
• PRACTICE B:
    50 km at 53.13º S of W       OR
    50 km at 36.87º W of S
           PROBLEMS 1 and 2
• Which of the following quantities are scalars, and
  which are vectors? (A) the acceleration of a
  plane as it takes off (B) the number of passengers
  on the plane (C) the duration of the flight (D) the
  displacement of the flight (E) the amount of fuel
  required for the flight?
• A roller coaster moves 85 m horizontally, then
  travels 45 m at an angle of 30° above the
  horizontal. What is its displacement from its
  starting point?(graphical techniques)
                  ANSWERS
•(A) vector (B) scalar (C) scalar (D) vector
•(E) scalar
126 m at 10° above the horizontal 126 m at
10° above the horizontal
                RESULTANT

                                      30°
            PROBLEMS 3 and 4
• A novice pilot sets a plane’s controls, thinking the
  plane will fly at 250 km/hr to the north. If the
  wind blows at 75 km/hr toward the southeast,
  what is the plane’s resultant velocity? Use
  graphical techniques.

• While flying over the Grand Canyon, the pilot
  slows the plane’s engines down to one-half the
  velocity of the last problem. If the wind’s
  velocity is still 75 km/h toward the southeast,
  what will the plane’s new resultant velocity be?
             ANSWERS
• 204 km/h at 75° north of east
• 89 km/h at 54° north of east
             PROBLEM
• The water used in many fountains is
  recycled. For instance, a single water
  particle in a fountain travels through an
  85 m system and then returns to the same
  point. What is the displacement of a
  water particle during one cycle?
         ANSWER
• ZERO

				
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posted:6/2/2011
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