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Rocket Launch: Function & Height & Velocity Graph

Rocket Launch: Function & Height & Velocity Graph
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2020-05-31 21:58
FunctionCoordinate GeometryCalculusDerivativeGraphing
This example demonstrates the graphical representation of height and velocity changes during a rocket launch. It involves core mathematical concepts such as functions, derivatives, sequences, coordinate geometry, and calculus. Key GeoGebra commands/objects used include Derivative, Sequence, RemoveUndefined, TableText, Max, Min, PolyLine, Textfield, and LaTeX for constructing the graph. Suitable for high school and above, ideal for physics and mathematics education.

GeoGebra Commands & Parameters

  1. Derivative(f) → f'
  2. Sequence((i, f'(i)), i, 0, floor((10 * xmaxdom)) / 10, floor((xmaxdom * 10)) / ((10 * n))) → LPv
  3. Sequence((i, f(i)), i, 0, floor((xmaxdom * 10)) / 10, floor((xmaxdom * 10)) / ((10 * n))) → LPp
  4. RemoveUndefined(Sequence[y(Element[LPv, i]), i, 1, Length[LPv], 1]) → LyV
  5. RemoveUndefined(Sequence[y(Element[LPp, i]), i, 1, Length[LPp], 1]) → LyP
  6. RemoveUndefined(Sequence[x(Element[LPp, i]), i, 1, Length[LPp], 1]) → LxP
  7. RemoveUndefined(Sequence[x(Element[LPv, i]), i, 1, Length[LPv], 1]) → LxV
  8. TableText({LaTeX[f, true, true]}, {LaTeX[f', true, true]}) → text1
  9. Max({Max[LxP], Max[LxV]}) → xmax
  10. Derivative(Expand[f]) → f'expand
  11. Min(LxP) → xmin
  12. Max({Max[LyP], Max[LyV]}) → ymax
  13. Min(LyP) → ymin
  14. PolyLine(Sequence[(i, f'(i)), i, 0, xmax, 0.01]) → f'rest
  15. PolyLine(Sequence[(i, f(i)), i, 0, xmax, 0.01]) → frest
  16. Textfield(v_e) → InputBox1
  17. Textfield(m_0) → InputBox2
  18. Textfield(u) → InputBox3
  19. LaTeX(xmaxdom, true, true) → text4
  20. Sequence((0, Element[LyP, i]), i, 1, Length[LyP], 1) → l1
  21. Textfield(n) → InputBox4