Head to Tail Vector Analysis

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Head to Tail Vector Analysis

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  1. Vector Analysis

    Slide 1 - Vector Analysis

    • Head-to-Tail Method
  2. Vector

    Slide 2 - Vector

    • Arrow drawn to represent a vector quantity (magnitude & direction)
    • Length indicates magnitude
    • Arrow points to indicate direction
  3. Compass Rose

    Slide 3 - Compass Rose

    • 0o or 360o
    • 45o
    • 90o
    • 135o
    • 180o
    • 225o
    • 270o
    • 315o
  4. Technique 1:  Drawn-To-Scale

    Slide 4 - Technique 1: Drawn-To-Scale

    • Decide upon a scale that will fit the page.
    • Draw each vector the length that indicates its magnitude.
    • Draw it pointing in the correct direction.
    • The “Resultant” is drawn from the head of the first vector straight to the tail of the last vector.
    • The magnitude of the answer is determined by measuring the Resultant and using the scale.
    • The direction of the answer can be determined by using a protractor.
  5. Simple Displacement Problem

    Slide 5 - Simple Displacement Problem

    • Sally leaves her house and walks 3 blocks East, then she walks 4 blocks South. What is her displacement from home?
    • N
    • scale:
    • 1 block = 1 cm
    • answer:
    • 5 blocks 53o South of East
    • -or-
    • 5 blocks @ 143o
    • 53o
    • 3 cm
    • 4 cm
    • 5 cm
  6. Technique 1:  Trigonometry

    Slide 6 - Technique 1: Trigonometry

    • Sketch vectors from problem.
    • Use Pythagorean theorem to find magnitude of resultant.
    • Use sin, cos, or tan to find angle.
    • Refer to compass rose to determine direction.
  7. Simple Displacement Problem

    Slide 7 - Simple Displacement Problem

    • Sally leaves her house and walks 3 blocks East, then she walks 4 blocks South. What is her displacement from home?
    • c2 = a2 + b2
    • c = (3 blocks)2 + (4 blocks)2
    • c = 5 blocks
    • 53o
    • 3 blocks
    • 4 blocks
    • 5 blocks
    • tan = opp/adj
    • = tan-1 (4 blocks / 3 blocks)
    • = 53o
    • answer:
    • 5 blocks 53o South of East
    • -or-
    • 5 blocks @ 143o