Homework Help: Rocket science in classical mechanics

1. Sep 16, 2008

jmnance

1. The problem statement, all variables and given/known data
a rocket propelled car has total mass m0 and empty mass (after all of the fuel is burned) of m1. the car's exhaust speed is u and it has a constant burn rate of a=-dm/dt. ignore friction of wheels on the road, assume road is horizontal, and ignore air res. the driver fires the rockets to accelerate from rest. after some time, he reverses the engines to decelerate the car back to zero speed. (the rocket engines are always firing either forward or backward.)

What is the mass of the car including the remaining fuel, at which the driver should reverse the engines in order to maximize the car's top speed? All fuel should be burnt at the end when the car's velocity is zero.

What is the speed of the car as a function of time?

2. Relevant equations
this is a general equation for rocket motion with no external force
v= u log(mo/m)
also, m=m0-at

3. The attempt at a solution

I really have no idea how to aproach this problem. I know that the fact that the fuel must be used up at exactly the velocity of zero has to play a huge role as a limiting factor. Thanks for the help guys!