Rocket Problem

[Midas_Touch]

Consider a rocket (initial mass m)o) accelerating from rest in free space. At first, as it speeds up its momentum p increases, but as its mass m decreases p eventually begins to decrease. For what value of m is p maximum?

So I started out with the rocket equation

which is

m*v' = m'*v_ex + F_ext

where,

v_ex - exhaust speed
F_ex = external force

since it is accelerating the external force is -mg.

I know that the momentum P(t) = mv.

So in order to show for what value of m is P maximum, then do I simply solve for v(t) and let t go to infinity?

[mathmike]

didnt you say it was in free space

then where did gravity come into play