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Ballistic Trajectory Demo

Ballistic Trajectory Demo
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2024-01-22 17:54
VectorFunctionCoordinate GeometryParametric Equation
In collections El dominio del Tiempo (cinemática intuitiva)
This example demonstrates the parabolic trajectory of an object under gravity, involving key math concepts like 2D vectors, coordinate geometry, parabola equations, parametric equations, and limits. Construction highlights include commands like Polygon, PointIn, Semicircle, Vector, PolyLine for trajectory building, and Angle, Segment, If for dynamic effects. Suitable for high school and above students studying physics and mathematics related to kinematics, function graphs, and parametric equations.

GeoGebra Commands & Parameters

  1. Polygon((0, 0), (0, 10^(6)), (10^(6), 10^(6)), (10^(6), 0)) → a, h, i, j, l
  2. PointIn(a) → A
  3. Semicircle(A + (0, r), A + (0, (-r))) → c
  4. Point(c) → P
  5. Vector(A, P) → v0
  6. Vector((x(M), y(A)), (x(M) + v0x, y(A))) → vx
  7. Vector((x(A), y(A)), (x(A), y(A) + v0y)) → vy
  8. PointIn(a) → B
  9. Textfield(r) → CasillaDeEntrada1
  10. Angle(A + (1, 0), A, P) → α
  11. Vector(M, M + v) → vv
  12. Segment(A, (x(A), y(A) + v0^(2) / ((2 * abs(g))))) → hArriba
  13. If(v0x ≟ 0 ∧ v0y ≥ 0, (v0y + sqrt(((2 * y(A - B)) * abs(g)) + v0y^(2))) / abs(g), v0x ≟ 0 ∧ v0y < 0, (v0y - sqrt(((2 * y(A - B)) * abs(g)) + v0y^(2))) / abs(g), x(B - A) / v0x) → Tteor
  14. Segment(A, (x(A), 0)) → hAbajo
  15. PolyLine(reg) → pol

AI Drawing Prompt Reference

Draw a ballistic trajectory demonstration. First establish a coordinate system with a rectangular boundary. Set a launch point A within the coordinate system, then draw a semicircle above the launch point. Take a point P on the semicircle and connect A to P to form the initial velocity vector. Decompose this vector into horizontal and vertical components. Set another point B as the target within the boundary. Based on the launch point, target point, and initial velocity, draw a parabola representing the object's flight path. Label the launch angle, theoretical flight time, and draw vertical lines showing the maximum height above the launch point and the ground level below. The entire graphic demonstrates parabolic motion under gravity.
The prompt above was compiled from the original drawing commands and is for reference only.