Problem $1$: $(30$ points$)$

Intelligence sources indicate that a new missile is under development from another nation. Observations of a test flight

of this vehicle reveal the following information

Nozzle exit diameter of $1$ m

Nozzle exit pressure $($inferred from plume shocks$)$ of $0\mathrm{.}8$ atm

Initial vehicle mass of $40,000kg$

Burn time of $100$ s

Propellant characteristics $($estimated from presumed propellant combination$)$ of $=1\mathrm{.}2$ and $c^{**}=1500\frac{m}{s}$

Trajectory information reveals the vehicle thrust increased $10\%$ from seal level to burnout altitude of $20$ km $.$ Assume

ideal performance, constant chamber pressure for the entire flight, expansion ratio of $10,$ and structure mass is $15\%$ of

propellant mass. Calculate the following

Part $($a$)(5$ points$)$

Part $($b$)(5$ points$)$

Part $($c$)(5$ points$)$

Part $($d$)(5$ points$)$

Part $($e$)(5$ points$)$

Part $($f$)(5$ points$)$

Engine thrust at sea level and burnout altitude

Engine chamber pressure

Nozzle throat diameter

Engine mass flow rate

Engine specific impulse at sea level

Payload mass