Show that if engine mass were a negligible part of the entire total mass of a rocket vehic...

Show that if engine mass were a negligible part of the entire total mass of a rocket vehicle, and if the total structural and engine mass were simply proportional to the initial propellant mass, the structural efficiency factorϵ would be independent of the mission ∆u. A single-stage solid-propellant booster has the following characteristics:

Show how the payload ratio λ and the structural efficiency ϵ depend on the mission velocity ∆u and compare your results for ϵ with Fig. 10.6. The definition of the structural factor in this case may be written

Here neglect gravity and drag effects.