3.1 Introduction to Vectors

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3.1 Introduction to Vectors

• Page 82

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Section Objectives

• Distinguish between a vector and a scalar.
• Add and subtract vectors by using the graphical
  method.

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Scalar Quantities

• Scalars can be completely described by magnitude
  (size)
• Scalars can be added algebraically
• They are expressed as positive or negative
  numbers and a unit
• examples include mass, electric charge,
  distance, speed, energy

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Vector Quantities

• Vectors need both a magnitude and a direction to
  describe them (also a point of application)
• They need to be added, subtracted and multiplied
  in a special way
• Examples - velocity, weight, acceleration,
  displacement, momentum, force

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Distinguish between a scalar and a vector.

• The acceleration of a plane as it takes off.
• The duration of a flight.
• The displacement of the flight
• The amount of fuel required for the flight.
• The force acting on the plane in the form of air
  resistance.

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3.2 Vector Operations

• Page 86

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Section Objectives

• Calculate the magnitude and direction of a
  resultant vector.
• Resolve vectors into components.
• Add vectors that are not perpendicular.

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Terminology

• Two or more vectors can be combined together to
  form a resultant
• A vector that does not lie along the x or y-axis
  may be resolved into its components

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Calculate the magnitude and direction of a
resultant vector.

• Draw 20? south of west.
• Draw 20? west of south.

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Calculate the magnitude and direction of a
resultant vector.

• Use the Pythagorean Theorem to find the magnitude
  of the resultant.

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Calculate the magnitude and direction of a
resultant vector.

• Use SOHCAHTOA to find the direction of the
  resultant.

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Resolve vectors into components.

• Every vector can be resolved into its x and y
  components using trigonometry.
• If a vector is located on the x or y axis, then
  the other component of that vector is zero.

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Resolve vectors into components.

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Add vectors that are NOT perpendicular

• If the original displacement vectors do not form
  a right triangle
• 1. Resolve each vector into its x- and
  y-components
• 2. Find the sum of the x- and y-components
• 3. Use the Pythagorean Theorem to find the
  magnitude of the resultant
• 4. Use the tangent function to find the direction
  of the resultant

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Adding non-perpendicular vectors
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Adding non-perpendicular vectors
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Practice 1

• A hiker walks 27.0 km from her base camp at 35?
  south of east. The next day, she walks 41.0 km
  in a direction 65? north of east and discovers a
  forest rangers tower. Find the magnitude and
  direction of her resultant displacement between
  the base camp and the tower.

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Check you work!

• Page 89
• 1. a) 23 km
• b) 17 to the east
• 2. 45.6 m at 9.5 east of north
• 3. 15.7 m at 22 to the side of downfield
• 4. 1.8 m at 49 below the horizontal

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Check your work!

• Page 92
• 1. 95 km/h
• 2. 44 km/h
• 3. x21 m/s, y5.7 m/s
• 4. x0 m , y5m

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Practice 1

• A bullet travels 85 m before it glances off a
  rock. It ricochets off the rock and travels for
  an additional 64 m at an angle of 36 degrees to
  the right of its previous forward motion. What
  is the displacement of the bullet during this
  path.

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Make physics YOUR business. Try problems 1-4 on
pages 94.
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Dr. Miller says Time for some practice! Try
pages 89 92.
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Check your work!

• Page 94
• 1. 49 m at 7.3 to the right of downfield
• 2. 7.5 km at 26 above the horizontal
• 3. 13.0 m at 57 north of east
• 4. 171 km at 34 east of north

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Problem 3C

• 1. 216.5 m at 30.0? north of east
• 2. 2.89 ? 104 m at 21.7? above the horizontal
• 4. 1320 km at 3.5? east of north
• 5. 221 km at 11.2? north of east

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Add and subtract vectors by using the graphical
method.
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Multiply and divide vectors by scalars.

• Multiplying or dividing vectors by scalars
  results in _________________.
• You are in a cab traveling 25 mph east. You tell
  the cab driver to drive twice as fast. Your new
  velocity is ____________________.
• You are in a cab traveling 25 mph east. You tell
  the cab driver to drive twice as fast in the
  opposite direction. Your new velocity is
  ________________.

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Add and subtract vectors by using the graphical
method.

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Add and subtract vectors by using the graphical
method.

• T / F Vectors can be added in any order.
• T / F Vectors can be moved parallel to
  themselves in diagrams.
• Lets see http//www.physicsclassroom.com/mmedia/
  vectors/ao.cfm

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Calculate the magnitude and direction of a
resultant vector.

• http//www.physicsclassroom.com/Class/vectors/u3l1
  b.cfm