Head to Tail Vector Analysis

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Slide 1  Vector Analysis
 HeadtoTail Method

Slide 2  Vector
 Arrow drawn to represent a vector quantity (magnitude & direction)
 Length indicates magnitude
 Arrow points to indicate direction

Slide 3  Compass Rose
 0o or 360o
 45o
 90o
 135o
 180o
 225o
 270o
 315o

Slide 4  Technique 1: DrawnToScale
 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.

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

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.

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
 = tan1 (4 blocks / 3 blocks)
 = 53o
 answer:
 5 blocks 53o South of East
 or
 5 blocks @ 143o