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2D Projectile Motion Animation with Velocity Vectors

2D Projectile Motion Animation with Velocity Vectors
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2016-06-09 20:05
VectorParametric EquationSlider AnimationLocusGraphing
① This example animates the path of a projectile in two dimensions, showing its instantaneous velocity vector at each point, making the physics of projectile motion visually intuitive. ② Core mathematical concepts include parametric equations, vector decomposition, uniformly accelerated motion under gravity, velocity composition and resolution, and the parabolic trajectory. ③ Construction highlights: using GeoGebra commands such as Line, Point, Rotate, Angle, Vector, and Translate to build the initial velocity vector, launch angle, and height; sliders control initial speed, direction, and height; animation buttons (AnimationOn, button1, button2) enable dynamic playback; the velocity vector is displayed via vector commands, with target and trajectory points (TARGET, P, Q) marked. ④ Suitable for high school physics or mathematics classes covering projectile motion, vectors, and parametric equations, as well as introductory university physics demonstrations to reinforce the concepts of motion decomposition and composition.

GeoGebra Commands & Parameters

  1. Line(A, xAxis) → a
  2. Point(a) → B
  3. Rotate(B, α, A) → B'
  4. Angle(B, A, B') → β
  5. Vector(A, C) → u
  6. Vector(O, Q) → v
  7. Translate(P, v) → P'
  8. Vector(P, P') → w

AI Drawing Prompt Reference

Create a 2D projectile motion animation. Start with a horizontal ground line and a launch point on it. From this point, a projectile moves along a parabolic trajectory with adjustable initial speed, launch angle, and height. Along the trajectory, mark several positions, and at each position draw an arrow representing the instantaneous velocity vector, decomposed into horizontal and vertical components (horizontal constant, vertical changing). Show the launch angle marker and the initial velocity vector from the launch point. Use sliders to control initial speed, angle, and height, and add play buttons to animate the motion with velocity vectors updating in real time.
The prompt above was compiled from the original drawing commands and is for reference only.