Level 5: Equations of falling

Gravity and orbits · level 5 of 8 · rough age 12-13 (a guide for parents; anyone can start anywhere)

In level 3 you found falling patterns from tables. In this level they become equations you can use for any height, any time and any planet. You derive \(s = \tfrac12 gt^2\) and \(v^2 = 2gs\), split a throw into across and up-and-down, work out a jump on Mars from your own jump at home, find terminal velocity from a balance of forces, and see how \(g\) changes as you climb.

Lesson	You will be able to
Distance fallen	Derive and use \(s = \tfrac12 gt^2\), and compare fall times on Earth and Mars
The speed of a fall	Use \(v = gt\) and \(v^2 = 2gs\) to find landing speeds, and match a fall on Mars to one on Earth
Projectiles	Split a throw into across and up-and-down, and find its time, height and range
The Mars jump, worked out	Find your take-off speed from a jump at home, and work out the same jump on Mars
Terminal velocity	Balance weight and drag to find a falling speed, and see why Mars falls are so fast
Gravity with height	Use \(g = g_0 R^2/(R+h)^2\) and its short form for small heights

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