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

1. Nov 22, 2009

### Proximity

1. The problem statement, all variables and given/known data
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 vy = uex * ln[M0 / M(t) ] - g * t. uex 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
Fth = 2.32E7 N (Force of thrust)
R = 4.6E3

M(t) = M0 - R * t
Fth = -R * uex

2. Relevant equations

?

3. 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)

Last edited: Nov 22, 2009
2. Nov 22, 2009

### Proximity

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

3. Nov 22, 2009

### D H

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

4. Nov 22, 2009

### Proximity

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

(Fth / m) - g = a

But m is dependent on time so that becomes:

[Fth / (m0 - R * t)] - g = a

Do I then have to integrate that somehow?

5. Nov 22, 2009

### Proximity

Anyone?

6. Nov 22, 2009

### D H

Staff Emeritus
How hard is that to integrate?

7. Nov 23, 2009

### Proximity

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