CHAPTER 3: TWO DIMENSIONAL MOTION

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CHAPTER 3 TWO DIMENSIONAL MOTION VECTORS

• SECTION 1
• INTRODUCTION TO VECTORS

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WHAT ARE VECTORS?

• Vectors are rays that have size and direction.
• To show vector addition graphically, you need to
  draw the vectors to scale.
• You need to be sure that you place the head of
  one vector on the tail of the other keeping in
  mind the direction.
• The red line is called the
  resultant.

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CHAPTER 3 TWO DIMENSIONAL MOTION VECTORS

• SECTION 2
• VECTOR OPERATIONS

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ADDING VECTORS ALGEBRAICALLY

• Adding vectors using algebra gives us a much more
  exact number than doing it graphically.
• To add vectors algebraically, you need to
  remember a little geometry and trigonometry!

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ADDING VECTORS ALGEBRAICALLY-Cont

• opposite
• side
• adjacent side
• sin ? opposite cos ? adjacent
• hypotenuse hypotenuse
• tan ? opposite
• adjacent

hypotenuse
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ADDING VECTORS ALGEBRAICALLY-Cont

• When vectors are at right angles to each other,
  we can find both the size and direction.
• We find the magnitude of the resultant by using
  the Pythagorean Theorem
• (a2 b2 c2 ).
• We find the direction (angle) of the resultant by
  using the tangent function

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COMPONENTS OF VECTORS

• When vectors are applied at different angles, we
  need to break them into their vertical (y) and
  horizontal (x) pieces.
• Once we do this, we can find the magnitude and
  direction of the resultant.
• Find net x and net y
• Use Pythagorean Theorem to find resultant size.
• (net x)2 (net y)2 r2
• Use tan ? net y to find resultant
• net x direction.

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COMPONENTS OF VECTORS

• The net x is the sum of the x components and
  the net y is the sum of the y components.
• The resultant is the vector that is located from
  the diagonal after completing the rectangle.

50 N force
30 N force
? 110o
? 60o
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CHAPTER 3 TWO DIMENSIONAL MOTION VECTORS

• SECTION 3
• Projectile Motion

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What is Projectile Motion?

• This is motion in 2 directions.
• The horizontal and vertical velocities of a
  projectile are independent of each other and can
  be studied separately to determine the position
  of objects that are thrown or launched.
• The path of a projectile is called its
  trajectory. The shape of this trajectory depends
  on the viewpoint of the observer but it is always
  some type of parabola.

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FORMULAS FOR PROJECTILE MOTION

• To find horizontal motion
• ? x vxt where x horizontal displacement
• vx initial
  horizontal velocity
• To find vertical motion
• y vyt 1gt2 where y vertical
  displacement
• 2 vy initial
  vertical velocity
• vyf vy gt where vyf final vertical
  velocity

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PROJECTILE MOTION CONT

• When objects are launched or thrown at an angle,
  the major force is in the vertical direction. At
  the top of the parabola, the object reaches its
  maximum height.
• The RANGE is the horizontal distance from the
  point of bounce until the projectile returns to
  surface height.
• You need to find vx vy by components.

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CHAPTER 3 TWO DIMENSIONAL MOTION VECTORS

• SECTION 4
• Relative Motion

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WHAT IS RELATIVE VELOCITY?

• Sometimes it appears that objects are moving
  faster or slower than they actually are because
  of a frame of reference.
• Since velocity is a vector (size direction), we
  need to consider these when determining relative
  velocity.
• vac vab vbc