$4\mathrm{.}1$ Starting with the generalized thrust equation, Eq$.(4\mathrm{.}5),$ find the uninstalled thrust $($lbf$)$ of the space shuttle main engine $($SSME$)$ of Problem $3\mathrm{.}11$ under the following conditions:

a$)$ At launch

b$)$ At the design altitude of $44,600ft$

c$)$ In a vacuum $($ambient pressure $=0)$

Recall that the uninstalled thrust is the net axial force produced by an engine in an idealized inviscid fluid. The SSME nozzle is choked at all these conditions. Be clear with all assumptions and their implications. Refer to Appendix C$,$ Table C$\mathrm{.}1.$