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.