### Still have math questions?

What fraction of its total initial mass would the rocket considered in Example $$1$$ have to burn as fuel in order to accelerate in a straight line from rest to the speed of its own exhaust gases? to twice that speed?
$$\frac { e - 1 } { e } , \quad \frac { e ^ { 2 } - 1 } { e ^ { 2 } }$$