Need help on Rocket Problem?

Question

I am having some difficulty proving the following equation of vertical motion of a rocket.

y=(Vexhaust * t) - (1/2g * t^2) - (m * Vexhaust * ln(m0 / m)) / k

Givin information:

F=trust-Fgravity

m(dV/dt)=Vexhaust(dM/dt)-mg

dM/dt changes at constant rate

dM/dt=-k

Therefore:

m=m0-kt

Thanks for the help. I've been working on this for 2 days.

Answer 1

As usual, it's hyperphysics to the rescue. See the ref. and click on "show" for derivations.