Hello please answer with step by step problem.

Problem $1$

A$)$ The total mass of a rocket can be broken down into three main components: the structural

weight of the rocket or empty mass $m_e,$ the mass of the propellent $m_p,$ and the mass of

the payload $m_{PL}.$ When describing rockets, we can define them in terms of their structural

ratio $,$ and their payload ratio $.$ These are given by

$=\frac{m_e}{m_e+m_p}=\frac{m_e}{m_0-m_{PL}}$

$=\frac{m_{PL}}{m_e+m_p}=\frac{m_{PL}}{m_0-m_{PL}}$

Using this information, rewrite the final velocity of the rocket from the rocket equation in

terms of $$ and $$ assuming that the final velocity is when all propellent has been burned.

B$)$ Using your derived equation from Part A$,$ create a logarithmic plot of the normalized final

velocity $\frac{v_f}{I_{sp}{g}_0}$ as a function of $$ ranging from $0\mathrm{.}0001$ to $1\mathrm{.}0$ for various values of $lon$

ranging from $0\mathrm{.}001$ to $0\mathrm{.}5.$

C$)$ Given that current materials allow for a lower limit of $=\mathrm{.}1$ and a payload ratio of $=$

$\mathrm{.}05$ discuss if a single$-$stage rocket would be a viable solution for leaving Earth's

atmosphere $($Assume a specific thrust of $I_{sp}=300s).$