Question $2$:

It may be desired to use a staged rocket even when the desired final velocity can be reached in a

single stage. In fact, one of the most contentious issues about launch systems is whether single$-$

stage$-$to$-$orbit is the way of the future. To help your thinking on this important matter, it is

suggested that you compare launch systems with $1,2$ and $3$ stages, using as a Figure of Merit the

ratio of Payload Mass $/$ Initial Mass.

To make the comparison simple, assume the following:

Final velocity: $8,000\frac{m}{s}$

Exhaust velocity, constant for all stages: $4,000\frac{m}{s}$

Structural weight fraction $($Structure Mass $/$ Initial Mass$)$ for all stages, including the

engine mass: $0\mathrm{.}07$

Initial acceleration fixed for all stages at $\frac{a_0}{g}=2.$