Problem $1(20$ points$)$

A chemical bipropellant rocket has the following properties: the ideal heat of combustion $($per

unit mass$)$ of the propellants in the chamber is $q_R=5374k\frac{J}{k}g,$ the combustion efficiency

is ${}_{\text{c}\text{o}\text{m}\text{b}}=0\mathrm{.}96,$ and the measured thrust is $F_t=890N.$

$($a$)(5$ points$)$ What is the specific impulse $I_{sp}$ required to achieve an internal efficiency of

${}_{\text{i}\text{n}\text{t}}=0\mathrm{.}92?$

$($b$)(5$ points$)$ If the rocket is loaded with $M_p=925kg$ of propellant so that the initial

$($wet$)$ mass is $M_0=1250kg,$ what is the $V$ that can be obtained by the vehicle in the

absence of external forces?

$($c$)(5$ points$)$ What is the total burn time $t_b,$ assuming the rocket is fired continually with

a constant mass flow rate until all propellant is exhausted?

$($d$)(5$ points$)$ What is the total impulse $I_{\text{t}\text{o}\text{t}}$ delivered to the vehicle?