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Relationship Between Rocket Speed and Flight Time

Relationship Between Rocket Speed and Flight Time
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2023-10-18 22:14
In collections Wiederholung: Direkte und Indirekte Proportionalität Indirekte Proportionalität
This example graphically demonstrates the indirect proportional relationship between a rocket's speed and flight time. Key mathematical concepts include proportions and function graphs. It uses commands like Polynomial, Locus, and Function in GeoGebra. Suitable for 5-6th grade students to learn about proportions and function graphs.

GeoGebra Commands & Parameters

  1. Point(Segment[PP, EndX]) → PV
  2. Textfield(input1) → InputBox1
  3. Textfield(input2) → InputBox2
  4. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  5. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {4, 10, 6, 7, 4, 10, 7, 0, 6, 3, 2, 10, 4, 6, 1, 5, 6, 3, 2, 10, 3, 1, 9, 8, 9, 5, 4, 4, 2, 6, 10, 1, 4, 5, 5, 2, 9, 9, 3, 8, 4, 1, 7, 10, 8, 6, 1, 8, 7, 2, 1, 4, 1, 8, 8, 1, 6, 9, 9, 0, 9, 9, 8, 9, 5, 2, 8, 0, 5, 10, 6, 3, 2, 9, 1, 5, 8, 1, 2, 9, 0, 6, 1, 6, 5, 6, 3, 3, 9, 4, 9, 2, 0, 3, 5, 1, 7, 0, 8, 8}
  6. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  7. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {9, 4, 7, 9, 5, 3, 1, 8, 6, 6, 0, 8, 1, 8, 5, 2, 7, 3, 8, 5, 4, 9, 6, 7, 0, 8, 3, 4, 0, 3, 8, 8, 2, 5, 2, 10, 3, 2, 0, 3, 9, 7, 3, 3, 1, 1, 7, 7, 7, 9, 5, 6, 9, 3, 0, 1, 5, 4, 3, 9, 3, 4, 9, 6, 10, 5, 0, 9, 5, 0, 0, 8, 3, 1, 10, 9, 8, 9, 1, 0, 4, 7, 5, 5, 10, 6, 7, 7, 3, 4, 5, 7, 5, 8, 2, 1, 6, 8, 5, 4}
  8. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  9. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  10. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  11. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  12. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  13. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  14. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  15. SpeechBubbleLeft(K, 7.55, 1.35) → poly1
  16. Segment(PP, EndY) → lineYaxis
  17. Distance(PV, PP) → v
  18. Point(Line[S, yAxis]) → W
  19. Segment(W, Z) → h
  20. Polygon(S, W, Z, T) → q3, s_2, w, z_1, t_1
  21. Spline(listPoints5, 3) → splineCompleted
  22. Spline(listPoints3, 3) → spline1
  23. Spline(listPoints4, 3) → spline2
  24. Polynomial({P1, P2, P3, P4, P5, P6, P7}) → f_1
  25. Sequence(PP + ((m * sizex), 0), m, 1, 5) → pointsX
  26. Sequence(PP + (0, (m * sizey)), m, 1, 9) → pointsY
  27. Zip(Segment[P + (0, -0.1), P + (0, 0.1)], P, pointsX) → linesx
  28. Segment(PP, EndX) → lineXaxis
  29. Sequence(Text[(("\textsf\footnotesize{" * ReplaceAll["" + ((m * 10)) + "", ".", ","]) * "}"), (x(PP) - 0.35, y(PP) + (m * sizey) - 0.34), true, true, -0, 1], m, 1, 9) → textY
  30. Zip(Segment[P + (-0.1, 0), P + (0.1, 0)], P, pointsY) → linesy
  31. Sequence(Text[(("\textsf\footnotesize{" * ReplaceAll["" + (((m * 5) * " 000")) + "", ".", ","]) * "}"), (x(PP) + (m * sizex), y(PP) - 0.8), true, true, -0, 1], m, 1, 5) → textX
  32. NumberSeparationComma(kmh) → kmhText
  33. Point(Line[S, xAxis]) → H
  34. Textfield(input3) → InputBox3