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I.5.3.3. Polygon rule

📚

Polygon rule is used for adding of several nonlinear vectors which do not have the same point of application, by going through the following steps:

  • Draw the first vector.
  • The second vector is drawn with the origin at the top of the first vector, keeping its direction.
  • The third vector is drawn with the origin at the top of the second vector, keeping its direction and so on, until we represent all vectors.
  • The resulting vector is the segment that is obtained by joining the origin of the first vector (0) with the vertex of the last vector. The resulting vector has the same vertex as the last vector vertex.
  • The value of the resulting vector is obtained by measuring its segment with the ruler and then multiplying by the given (chosen) standard.
🔓 Solved problem

1. A cyclist goes 20 km East, then 40 km South, then 80 km West and 60 km North. Determine the resulting vector, ie how far the cyclist is compared with th initial point of departure (0).

Solution:

d1 = 20 km, horizontal direction, to the right

d2 = 40 km, vertical direction, down

d3 = 80 km, horizontal direction, to the left

d4 = 60 km, vertical direction, upwards

Standard: 1 cm : 10 km.

  • We represent the first movement vector d1. We put the second vector at the top of the first vector, and so on, until we represent all four vectors.

  • The resulting vector is the segment obtained by joining the origin (0) with the vertex of the last vector. The resulting vector has the same vertex as the last vector vertex.

  • The value of the resulting vector is obtained by measuring its segment with the ruler and then multiplying by the given standard: d = 6,3 ∙ 10 = 63 km. So the cyclist is at a distance of 63 km from the starting point, after the whole race.