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Velocity Addition I

Velocity Addition I
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2017-12-05 18:23
VectorTrigonometryGeometric ConstructionGraphing
This example demonstrates the principle of velocity addition, illustrating the resultant velocity by vector addition of two velocities. It involves core mathematical concepts like vectors, trigonometry, and geometric constructions. The construction uses commands such as Point, Segment, CircleArc, Intersect, Ray, OrthogonalLine, Angle, Line, Circle. Suitable for high school physics and mathematics education to understand vector addition and geometric relationships.

GeoGebra Commands & Parameters

  1. Point(yAxis) → R
  2. Point(yAxis) → A
  3. Segment(A, S) → i
  4. Point(xAxis) → C
  5. Point(yAxis) → B
  6. CircleArc(A, R, B) → c
  7. Intersect(c, i) → T,
  8. Ray(A, C) → b
  9. OrthogonalLine(C, b) → d
  10. CircleArc(A, C, T) → Arc
  11. Angle(C, A, Rotate[C, alfa, A]) → α
  12. OrthogonalLine(T, yAxis) → j
  13. OrthogonalLine(T, xAxis) → l
  14. Intersect(j, yAxis) → U
  15. Intersect(l, xAxis) → V
  16. Segment(A, V) → cosinus
  17. Segment(A, U) → sinus
  18. Segment(U, T) → s
  19. Segment(V, T) → t
  20. Segment(C, S) → tangens
  21. Point(yAxis) → L
  22. Point(d) → M
  23. Segment(A, J) → m
  24. Intersect(c, m) → O,
  25. OrthogonalLine(O, yAxis) → n
  26. OrthogonalLine(O, xAxis) → p
  27. Intersect(p, xAxis) → P
  28. Intersect(n, yAxis) → Q
  29. Segment(C, J) → q
  30. Segment(A, Q) → r
  31. Segment(A, P) → b_1
  32. Angle(J, A, V) → β
  33. Segment(P, O) → e
  34. Segment(O, Q) → f
  35. CircleArc(A, O, C) → g
  36. Segment(T, S) → a
  37. Segment(J, O) → h
  38. Segment(V, Q) → k
  39. Line(C, k) → a_1
  40. Intersect(a_1, yAxis) → F
  41. Line(F, xAxis) → c_1
  42. Line(S, xAxis) → d_1
  43. Point(d_1) → G
  44. Line(G, yAxis) → e_1
  45. Intersect(e_1, c_1) → H
  46. Segment(G, H) → v_1
  47. Segment(G, S) → g_1
  48. Segment(H, F) → h_1
  49. Segment(F, C) → i_1
  50. Segment(I, A) → f_1
  51. Line(N, yAxis) → j_1
  52. Circle(N, Ea / 5) → k_1
  53. Circle(Z, Eb / 5) → p_1
  54. OrthogonalLine(S, j_1) → l_1
  55. Segment(V, Q) → m_1
  56. Line(C, m_1) → n_1
  57. Intersect(yAxis, n_1) → B_1
  58. Intersect(l_1, j_1) → C_1
  59. OrthogonalLine(B_1, j_1) → q_1
  60. Intersect(j_1, q_1) → D_1
  61. Segment(C, B_1) → r_1
  62. Segment(B_1, D_1) → s_1
  63. Segment(C_1, S) → t_1
  64. Segment(C_1, D_1) → v_{ab}