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Parabola in Sports and Golf

Parabola in Sports and Golf
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2020-01-12 16:23
VectorCoordinate GeometryParametric Equation
This example demonstrates the application of parabolas in sports, particularly in golf ball trajectories, and real-life scenarios. Key mathematical concepts include parabolas, vectors, parametric equations, and coordinate geometry. The construction utilizes GeoGebra commands and objects such as Intersect, Circle, Rotate, Segment, OrthogonalLine, Line, Point, LineBisector, If, Vector, Tangent, Function, Polygon, and Angle. It is suitable for high school and above students to learn and understand the practical applications of parabolas, useful for physics and mathematics education.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(c, xAxis, 2) → B
  4. Rotate(B, α, A) → C
  5. Segment(A, C) → a
  6. Circle(C, 0.2) → d
  7. OrthogonalLine(C, a) → b
  8. Intersect(d, b) → D, E
  9. Circle(A, 0.3) → e
  10. Intersect(e, xAxis, 1) → F
  11. Intersect(e, xAxis) → G, H
  12. Circle(A, 0.2) → g_3
  13. Line(E, a) → h
  14. Intersect(g_3, h, 1) → I
  15. Segment(E, I) → i
  16. Segment(E, C) → j
  17. Line(D, h) → k
  18. Intersect(g_3, k, 1) → J
  19. Segment(D, J) → l
  20. Intersect(l, xAxis) → K
  21. Point(xAxis) → M
  22. Point(xAxis) → P
  23. Intersect(s, xAxis) → W, Z
  24. Segment(W, Z) → Distance
  25. LineBisector(W, Z) → b_1
  26. OrthogonalLine(X_0, Distance) → t_1
  27. Intersect(Distance, t_1) → C_1
  28. Segment(X_0, C_1) → g_1
  29. If(α < 90, 0, H_2) → u
  30. If(α ≟ 90°, H_2) → H_M
  31. Segment(H_M, A) → j_1
  32. Vector(W, W + ((v_0 / 4 * cos(α)), (v_0 / 4 * sin(α)))) → v_1
  33. Tangent(X_0, f) → m
  34. Circle(X_0, v_0 / 4) → p
  35. Intersect(p, m) → L, S
  36. Vector(X_0, S) → v
  37. Function(f, 0, Distance) → f1
  38. Point(xAxis) → H1
  39. Point(xAxis) → I1
  40. Point(xAxis) → J1
  41. Polygon(I1, J1, K1, L1) → poly5, i1, j1, k1, l1
  42. Point(xAxis) → U
  43. Angle(U, W, W + ((v_0 / 4 * cos(α)), (v_0 / 4 * sin(α)))) → β

AI Drawing Prompt Reference

Draw a graph showing the application of parabolas in sports, particularly golf ball trajectories. Include a circle and its tangent, along with points and line segments to represent the parabolic trajectory. Start by drawing a circle, find its intersections with the x-axis, then construct line segments and angles by rotating and connecting points. Finally, use points and line segments to represent the parabolic trajectory and the golf ball's motion path.
The prompt above was compiled from the original drawing commands and is for reference only.