Please pls provide a clear and step by step solution. Will rate if correct

If the mass flow in a rocket is constant, then the mass of the rocket can be modeled as $m=m_0-m_e^{}t$

where $m_e^{}$ is the mass flow rate exiting the rocket. We will assume that gravity acts on the rocket but not

drag.

A$)$ Derive an equation for the burnout velocity $($once all fuel has been consumed$),$ given that $m_f=$

$m_0-m_e^{}{t}_b$ where $t_b$ is the burnout time and velocity is given by

$v=g_0{I}_{sp}ln(\frac{m_0}{m_f})-{\displaystyle \underset{t_i}{\overset{t_f}{}}}{g}_{0}dt$

B$)$ From your derived equation in Part A$,$ what would be the best way for a rocket to burn fuel to

achieve the highest possible speed? How realistic is this approach?