积极 AI Logo 积极 AI

速度合成演示

速度合成演示
几何画板及绘图内容加载中，请稍等……
2017-12-05 18:23
向量三角函数几何作图函数图像
①本范例演示了速度合成原理，通过向量加法展示两个速度的合成效果；②涉及的核心数学概念包括向量、三角函数和几何作图；③作图要点——从下方『构造摘要』提炼用到了Point, Segment, CircleArc, Intersect, Ray, OrthogonalLine, Angle, Line, Circle等GeoGebra命令/对象；④适合高中物理和数学教学，用于理解向量合成与几何关系。

GeoGebra 命令及参数

  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}