Parabolic motion
This activity belongs to the GeoGebra book The Domain of the Time.
This animation simulates the parabolic motion of an object (like the launch of a projectile or the "flat" throw of a ball) in real time, neglecting air resistance, with a given initial velocity v0. The animation does not use formulas (neither equations, trigonometry, nor differential calculus) and only performs the necessary variations in the vectors that direct the motion.
- Note: Strictly speaking, this motion is not parabolic but elliptical. For it to be truly parabolic, either the gravitational acceleration g must be exactly constant, or the initial velocity v0 must be equal to the escape velocity of the Earth (about 40,280 km/h). However, near the Earth's surface and for small velocities, we can assume (as we have been doing) that the magnitude of g remains constant (approximately 9.81 m/s²), so the elliptical arc is practically identical to the parabolic arc.
SCRIPT FOR SLIDER anima
# Calculate the elapsed seconds dt; add one second if t1(1) < tt
SetValue(tt, t1(1))
SetValue(t1, First(GetTime(), 3))
SetValue(dt, (t1(1) < tt) + (t1(1) − tt)/1000)
# Move M
SetValue(v, v + dt g)
SetValue(M, If(y(M + dt v) > 0, M + dt v, Intersect(Line(M, M + v), xAxis)))
StartAnimation(anima, y(M) > 0)
# Registers M for the polyline trace
SetValue(reg, Append(reg, M))
Author of the activity and GeoGebra construction: Rafael Losada.