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Ball Bouncing in a Cube

Ball Bouncing in a Cube
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2015-01-01 01:11
VectorCoordinate GeometrySolid Geometry
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This example simulates a ball's 3D motion within a cube, moving at a constant speed in the horizontal direction while experiencing gravitational acceleration in the vertical direction. Key mathematical concepts include vectors, trajectories, and coordinate geometry. It utilizes commands like Polygon, Prism, and Sphere, suitable for high school physics and mathematics education.

GeoGebra Commands & Parameters

  1. Polygon((-3, -3, 0), (3, -3, 0), (3, 3, 0), (-3, 3, 0)) → poly1, a, b, c, d
  2. Prism(poly1, 6) → e, A, edge1, edge2, edge3, edge4, edgeAB, edgeBC, edgeCD, edgeAD, B, C, D, face1, face3, face4, face2, faceABCD
  3. Circle((x1, y1, 0), 0.2, xOyPlane) → g
  4. Circle((x1, y1, 6), 0.2, xOyPlane) → h
  5. Circle((x1, 3, 5.5 - z1^(2)), 0.2, x = 0) → k
  6. Sphere((x1, y1, 5.5 - z1^(2)), 0.5) → f
  7. Circle((x1, (-3), 5.5 - z1^(2)), 0.2, x = 0) → p
  8. Circle(((-3), y1, 5.5 - z1^(2)), 0.2, y = 0) → q
  9. Circle((3, y1, 5.5 - z1^(2)), 0.2, y = 0) → r

AI Drawing Prompt Reference

Draw a cube with side length 6 on the xOy plane. Inside the cube, draw a ball moving in the positive x direction, experiencing gravitational acceleration in the negative y direction. The ball starts at a position on the positive x-axis and negative y-axis, with z at 0. The ball's trajectory is represented by circles with a radius of 0.2, whose centers follow the ball's movement while the radius remains constant.
The prompt above was compiled from the original drawing commands and is for reference only.