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High Dive Problem

High Dive Problem
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2019-01-09 06:06
TrigonometryParametric EquationGeometric Construction
This example demonstrates a high dive problem involving trigonometric functions and parametric curves. By adjusting parameters, the impact of the diving height and angle on the distance can be observed. Commands such as Sequence, FitPoly, NSolutions, If, Textfield, Circle, Segment, and Polygon are used in construction. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Sequence((s(t), f_1(t)), t, Max[0, a - 5], a + 5) → l2
  2. FitPoly(l2, 2) → g_1
  3. NSolutions(g_1(x) = 0) → l3
  4. If(t < a, A, B) → C
  5. Textfield(a) → InputBox1
  6. Circle((0, k), r) → c
  7. Segment((0, k), (-50, 0)) → f
  8. Segment((0, k), (50, 0)) → g
  9. Textfield(r) → InputBox2
  10. Textfield(k) → InputBox3
  11. Textfield(p) → InputBox4
  12. Textfield(d) → InputBox5
  13. Textfield(b) → InputBox6
  14. Textfield(h) → InputBox7
  15. Polygon((x(D) - q / 2, y(D)), (x(D) + q / 2, y(D)), (x(D) + q / 2, 0), (x(D) - q / 2, 0)) → q1, i, j, l, m
  16. Textfield(q) → InputBox8
  17. Segment((x(D) - q / 2, 0), (x(D) - q / 2, y(D))) → n
  18. If(y(C) > 0, C, (Min[l3], 0)) → E
  19. Sequence(Segment[(0, k), ((r * cos((((2 * π) * t)) / p + (ss * rad))), (r * sin((((2 * π) * t)) / p + (ss * rad))) + k)], ss, 0, (2 * π), π / 7) → l1

AI Drawing Prompt Reference

Draw a high dive problem diagram, including a circle centered at the origin with radius r controlled by an input box, and two line segments from the circle center to the x-axis with length 50. Draw a parametric curve on the circle with parameter t and angle (2πt/p + ss), where p and ss are controlled by input boxes. Adjust parameters to observe the intersection points of the curve with the x-axis. Use input boxes to control the diving height k and angle a, and observe changes in the diving distance.
The prompt above was compiled from the original drawing commands and is for reference only.