A single$-$stage rocket has the following design parameters:

i$.$ Combustion chamber temperature $=4000K$

i$.$ Combustion chamber pressure $=5$MPa

ii$.$ Nozzle throat area $=0\mathrm{.}0008m2$

N$.$ Nozzle exir area $=0\mathrm{.}01m2$

v$.$ Propellant mass $=35kg$

vi$.$ Total mass at takeoff $=50kg$

vi$.$ Gas constant $=300$JikgK

vil. Ratio of specific heats $=1\mathrm{.}35$

Find the rocket height assuming aerolynamic drag is neglected and gravity does not vary:

a$.548m$

c$.573m$

b$.347m$

d$.485$m