We would like to send a certain payload to an altitude of $$400$$$km$ using a rocket $($reminiscent of a Space X Falcon $9$ FT $).$ Consider a

difference equation model describing the evolution in time of the vertical velocity $v$ and displacement $d$ of the rocket. Assume all constants

to be defined according to the International System of units $($i$.$e$.,$ meters, kilograms and seconds$).$

$v(n+1),=v(n)-t*g+\frac{t}{m}b$

$d(n+1),=d(n)+t*v(n)$

where $g$ is the gravitational acceleration assumed constant and equal to $9\mathrm{.}8\frac{m}{s^2}($in reality it decreases with the square of the distance

from the center of the earth$),t=0\mathrm{.}1s,m$ is the total mass of the rocket plus payload equal to $500,000kg$ and $b$ is the rocket trust in

Newtons defined as

$b,=7,607,000ifn{n}_b$

$b,=0ifn>n_b$

$($a$)-$ State the objective of the model and list inputs and outputs.

$($b$)-$ Write a python code to solve the model and determine the minimum value of $n_b$ leading to a maximum altitude of $400$ km $($don$\text{'}$t

worry if the rocket crashes to the ground after reaching the desired altitude$).$

$($c$)-$ Criticize the results obtained, the model and suggest possible improvements.

NOTE: please use Jupyter notebook for python coding screenshots if possible, thank you!