Unusual difficult kinetic problem

[dirk_mec1]

Homework Statement

http://img80.imageshack.us/img80/1797/20799357.png

Homework Equations

General kinetics formulas

The Attempt at a Solution

Actually I don't know how to start. The initial mass is M when qm energy is used the mass is M-m. If I use an energy balance I must use the integral version, right?

$$\int m(t) v \mbox{d}v = qm$$

But I don't know how to start.

 

[rock.freak667]

I myself have never done this before, but I will try to help you. I think my way should get the required formula.

Consider the exhaust gases (a small amount 'dm') at time 't'.

Initial momentum p_t= dm*v_e

Final momentum p_t+dt = dm(v_R-v_e)

Rocket:

p_t=(M-dm)v_R
p_t+dt= (M-dm)(v_R-v_e).

Now use conservation of momentum here: Loss in change of momentum in gas = change momentum gained by rocket

Using this, you should now be able to get a differential equation to solve (remember, 'dm' is infinitesimally small)