Accelerating rocket w/ changing mass *need to finish tonight*

[Proximity]

Homework Statement

Prove that the upward velocity of a rocket of initial mass M₀, which is propelled by fuel burning at a rate of R kg/s, is given by v_y = u_ex * ln[M₀ / M(t) ] - g * t. u_ex is the speed of the exhaust gas relative to the rocket and M₀ is the initial mass (rocket + fuel).

Also find the initial velocity and acceleration and velocity at time = 180s.

M₀ = 2.12E6 kg
F_th = 2.32E7 N (Force of thrust)
R = 4.6E3

M(t) = M₀ - R * t
F_th = -R * u_ex

Homework Equations

?

The Attempt at a Solution

Well it seems like I can get all the required values I need, but I still need to prove the given formula, and I'm not really sure where to start and I'm hoping for some tips.EDIT: Would finding the rate of changing for the rocket's acceleration be a start? (ie x m*s^3)

 

[Proximity]

No one can provide any help? I desperately need some.

 

[D H]

EDIT: Would finding the rate of changing for the rocket's acceleration be a start? (ie x m*s^3)

Finding the rocket's acceleration would be a good start.

 

[Proximity]

So applying Newton's second law I ended up with:

(F_th / m) - g = a

But m is dependent on time so that becomes:

[F_th / (m₀ - R * t)] - g = a

Do I then have to integrate that somehow?

 

[Proximity]

Anyone?

 

[D H]

So applying Newton's second law I ended up with:

(F_th / m) - g = a

But m is dependent on time so that becomes:

[F_th / (m₀ - R * t)] - g = a

Do I then have to integrate that somehow?

How hard is that to integrate?

 

[Proximity]

It's been a while since I've taken calculus, I'm not really sure how to.