[color=#0000ff][i][color=#0000ff][i][color=#999999]This activity belongs to the GeoGebra book [url=https://www.geogebra.org/m/mes4bgft]The Domain of the Time[/url].[/color][/i][/color][/i][/color][br][br]This animation simulates [b]real-time[/b] [i]free fall[/i] motion, ignoring air resistance. The animation [b]doesn't use formulas[/b] (neither equations nor differential calculus), it simply performs the necessary variations in the vectors that direct the motion.[br][br]A mass, represented by the blue point, falls from the initial position. [b][color=#cc0000]As Galileo discovered, the fall time doesn't depend on the mass[/color][/b]. Here we can observe the fall, both on Earth (without considering air resistance) and on the Moon.[br][br]At each moment, the animation changes both the velocity vector [b][color=#cc0000]v[/color][/b] (in red) and the position [color=#0000ff]M[/color] of the mass [i]m[/i] due to the action of gravity, represented by the vector [b][color=#6aa84f]g[/color][/b] (in green).[br][br]For this, every time a small amount of time [i]dt[/i] passes, by the definition of [i]acceleration[/i], the velocity increases by [i]dt[/i][b] [color=#6aa84f]g[/color][/b]. It's that simple; just add the following instruction to the script for the slider [b]anima[/b] ([i]Newton's 2nd law[/i]):[br][br] SetValue([b][color=#cc0000]v[/color][/b], [b][color=#cc0000]v[/color][/b] + [i]dt[/i] [b][color=#6aa84f]g[/color][/b])[br][br]Note: You can stop the animation at any time, but if you do, you must press the [img]https://www.geogebra.org/resource/hwdawgnn/MmhoDfF5M6lNH9D4/material-hwdawgnn.png[/img] button to update the time counter.[br][list][*][color=#999999]Note: By measuring time in seconds ([color=#999999][color=#999999][b]s[/b][/color][/color]), distance will be measured in meters ([color=#999999][color=#999999][b]m[/b][/color][/color]), velocity in [color=#999999][b]m/s[/b][/color], and acceleration in [color=#999999][b]m/s[sup]2[/sup][/b][/color].[/color][/*][/list]

[b]SCRIPT FOR SLIDER anima[/b][br][br][color=#cc0000][color=#cc0000]# Calculate the elapsed seconds dt; add one second if t1(1) < tt[/color][/color][br][color=#999999]SetValue(tt, t1(1))[br]SetValue(t1, First(GetTime(), 3))[br]SetValue(dt, (t1(1) < tt) + (t1(1) − tt)/1000)[/color][br][br][color=#cc0000]# Move M on Earth and M' on the Moon[/color][br][color=#0000ff]SetValue(v, v + dt g)[/color][color=#999999][br][color=#999999][color=#0000FF][color=#0000ff]SetValue[/color](v', v' + dt g')[/color][/color][br]SetValue(M, M + dt v)[br][color=#0000FF][color=#0000ff]SetValue[/color](M', M' + dt v')[/color][br][br][br][br][br][color=#999999][color=#999999][color=#0000ff][color=#0000ff][color=#999999][color=#999999]Author of the activity and GeoGebra construction: [/color][/color][/color][color=#0000ff][color=#999999][color=#999999][url=https://www.geogebra.org/u/rafael]Rafael Losada[/url].[/color][/color][/color][/color][/color][/color][/color]