Earlier we considered a rocket fired in outer space where there is no air resistance and where gravity is negligible. Suppose instead that the rocket is accelerating vertically upward from rest on the earth's surface. Continue to ignore air resistance and consider only that part of the motion where the altitude of the rocket is small so that g may be assumed to be constant.
a) How is eq. (8.37) modified in the presence of the gravity force?
b) Derive an expression for the acceleration a of the rocket, analogous to Eq. (8.39)
eq (8.37): m(dv/dt) = - vex(dm/dt)
m= mass of rocket vex= velocity of rocket exhaust v= velocity of rocket
eq (8.39): a= (dv/dt) = (-vex/m)(dm/dt)
The Attempt at a Solution
For part (a) I believe I need to factor in the impulse of gravity, Jg= mg(dt), but I don't know how. Then I would use my answer to part (a) to find an equation for acceleration.