2.25 pts. Consider a single-stage rocket with total initial mass M, constant ejection velocity u, and non-constant mass flow rate described by n = 2.12 for 0 < t < t where t is time to and t is the burnout time. Throughout the problem, neglect the (pe - PaA) term in the expression for the thrust, gravity, and drag.
a) Develop two expressions a = a for the rocket acceleration as a function of the dimensionless time T.
b) Develop expressions Tmar = Tmar and Tmar = Tmar for the value Tmar corresponding to the time when the acceleration reaches a maximum.
c) Determine the ranges of M and u for which the maximum acceleration occurs in the interval 15 < T < 150.
Vertical axis e) Discuss the plots corresponding to the limit values of M. Note the assumptions n const and u = const imply const. This is a highly unlikely scenario as we will see in our study of thrust chambers. M and u are tightly coupled, and it would be very hard to vary one without the other. This is just an exercise to study the effect of n along.
