1. Aug 22, 2008

### noppawit

Consider a rocket that is in deep space and at rest relative to an inertial reference frame. The rocket's engine is to be fired for a certain interval. What must be the rocket's mass ratio (ratio of initial to final mass) over that interval if the rocket's original speed relative to the inertial frame is to be equal to (a) the exhaust speed (speed of the exhaust products relative to the rocket) and (b) 2.0 times the exhaust speed?

In this problem, it is about momentum. So I think I can use only P=mv equation.

I tried by let M=rocket's mass, V=rocket's velocity, m=exhaust's mass, v exhaust's velocity

For (a) I start: $$\sum$$Pi = $$\sum$$Pf
----------->>>>>> (m+M)(Vi) = MVf-mvf

For (b) I start: $$\sum$$Pi = $$\sum$$Pf
----------->>>>>> (m+M)(Vi) = MVf-m*2vf

Am I correct? If yes, I don't know how to solve this equation until I get $$\frac{m+M}{M}$$ = ......................