Rocket Fuel Problem: Calculating Minimum Fuel Fraction for Rocket Broom Flight

[Bugeye]

Homework Statement

A warlock testing a rocket broom takes off from a standing start and flies at fixed elevation. The warlock and fueled rocket system start out with mass Mi. The rocket fires with exhaust speed u, losing mass at a constant rate R, and we’ll assume air drag is negligible. If the rocket broom is to reach a velocity equal to 0.6u, what minimum fraction of the initial mass must be devoted to fuel?

Homework Equations

Conservation of momentum

The Attempt at a Solution

I really don't even know how to start. I looked at this topic but I do not understand how the fuel has initial momentum, or how to apply any of that in another situation

 

[tiny-tim]

Welcome to PF!

Hi Bugeye ! Welcome to PF!

The rocket fires with exhaust speed u…
…
… I do not understand how the fuel has initial momentum

The question means that the difference in speed between the rocket and the fuel that's just gone is u.

So call the mass "m" (as a function of t), and write a formula for what happens when a mass dm of fuel is expelled in time dt …

what do you get? ​

(all the other smilies say "hi!" too :zzz: :shy: :!) )