Question $1$:

Our in$-$class discussion suggested multi$-$staging as a solution if a single$-$stage rocket was not

capable of reaching the desired velocity. Assume a rocket of total mass $100$ tons, carrying a

spacecraft payload of $1$ ton $.$ The engines develop a constant exhaust velocity of $3,000\frac{m}{s}.$ The

structural mass is assumed to be $10\%$ of the propellant mass.

Determine the velocity of this configuration as a single stage rocket

If the rocket is divided into two smaller stages, each with half the fuel, and the

structural mass also shared equally, and the payload being the same, determine the

total velocity increment for the two$-$stage configuration.

Repeat part $(2),$ assuming $3$ stages. What do you notice about the total velocity

increment as you add more and more stages? As an engineer, how would you

determine how many stages to use?