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Projectile Motion with Resistance

Projectile Motion with Resistance
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2020-07-13 10:49
VectorFunctionCoordinate Geometry
This example compares the trajectory of a projectile without resistance to one with resistance proportional to its velocity. Key mathematical concepts include vectors, functions, and coordinate geometry. Using GeoGebra commands like Vector and CurveCartesian, users can dynamically adjust initial velocity, launch angle, and resistance coefficient to observe trajectory changes. Suitable for high school physics and mathematics education.

GeoGebra Commands & Parameters

  1. Vector(P, V) → v
  2. Vector(P, A) → a
  3. CurveCartesian(((V_{initial} / ((-k)) * cos(α)) * ℯ^((-((k * t))))) + (V_{initial} / k * cos(α)), ((-((V_{initial} / k * sin(α)) + g / k^(2))) * ℯ^((-((k * t))))) - (g / k * t) + (V_{initial} / k * sin(α)) + g / k^(2), t, 0, t_{max}) → b
  4. CurveCartesian(((V_{initial} * cos(α)) * t), ((V_{initial} * sin(α)) * t) - ((g * t^(2))) / 2, t, 0, t_{max}) → c