Moving downwards with speed u and acceleration g, if I start thrusting with acceleration -a, how far do I travel (s) before my speed equals zero?

Then, as I'm falling I can recaculate with u = current v, and when s = current height I can turn my engine on and reach the ground when my speed is 0 (ignoring for now that my thrust changes as I use up fuel)

v² = u² + 2as
v² - u²  = 2as
(v² - u²)/2a = s
-u²/2(g-a) = s

Check that the units make sense

(ms⁻¹)²/ms⁻² = m
m²s⁻²/ms⁻² = m
m=m

Yup, that checks out. Time to give it a try.

I've picked up Kerbal again, still playing with the kOS plugin. This time, instead of going straight for orbit, I've spent a bit of time messing around with sub-orbital hops (which has got me lots of lovely science!).

I've also written a landing script that slams the engines on at just the right height to reach zero velocity at the surface. I've tasted it on Kerbin and it's looking good, next stop Mun!

However, I can't put it off any longer, next session is orbit or bust!

(The maths posted at 14:22 today works btw, it's correctly calculating the hight I need to turn my engines on at.(Which is quite scarily close to the ground, I can tell you!)