Obviously, we can make rockets to go very fast, but what is a reasonable top speed? assume that a rocket is fired from rest at a space station in deep space, where gravity is negligible. assume that c = 3.00 108 m/s.

I’ve answered this problem before and there were 2 parts in this problem.

The solution would be like this for this specific problem:

A.    Vf = Vi + Vex*ln(Mi / Mf) 
0.002 * 3e8m/s = 0 + 2000m/s * ln(Mi / Mf) 
300 = ln(Mi / Mf) 
1.9e130 = Mi / Mf 

B.    4000m/s = 2000m/s * ln(Mi / Mf) 
2 = ln(Mi / Mf) 
7.389 = Mi / Mf 
Mf = Mi / 7.389 = 0.135*Mi