Height as a function of time

[Froggy]

Basically what you've got is a mass point with zero volume which you drop from a certain height (h) so it starts falling downwards. What I need is a function of height in relation to time of the drop. The trick is g (gravity acceleration) is not a constant, it increases with time (or with distance travelled)

h(t) = ?
g(t) = ?
g(h) = ?

I'd appreciate any help, and if you can ad some explanation.

 

[tango92]

g is a constant. unless your talking about ridiculously large heights bordering on the edge of space in which case g will increase. and that derivation is too complex for me to do right now (its 6 am here, im revising for an exam and wasted lol)

presuming g is constant

h(t) = (1/2)(G)(t^2)

just rearrange to find the others

 

[Froggy]

Lol I know how do do it if g is a constant, I'm looking for the derivation, yes.
Thanks though.