# Homework Help: Unusual difficult kinetic problem

1. Sep 27, 2010

### dirk_mec1

1. The problem statement, all variables and given/known data
http://img80.imageshack.us/img80/1797/20799357.png [Broken]

2. Relevant equations
General kinetics formulas

3. 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.

Last edited by a moderator: May 4, 2017
2. Sep 27, 2010

### 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 pt= dm*ve

Final momentum pt+dt = dm(vR-ve)

Rocket:

pt=(M-dm)vR
pt+dt= (M-dm)(vR-ve).

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)