A rocket having mass $M$ is launched vertically with a trust force $.$

Model b$)$ Assume that the mass of the rocket $M=1000$ and the gravity $g=9\mathrm{.}81$ are constant. Derive

the dynamic model of the rocket with the trust actuator, The mass of the rocket converges to $M=70$

in $1000$ seconds due to fuel consumption where the g becomes zero at the space. Modify the model

in model b$.$ explain the mechanical problem with a differential equation convert the differential equation you found to the s domain and find the transfer function and draw the step response in matlab.