Problem $2(30$ points$).$ As an aircraft propels through the skies at supersonic velocities, the aerodynamic drag force $F_D$ exerted upon it is intricately governed by a combination of the speed of sound $c,$ its own velocity $V,$ the ambient air density $,$ and a characteristic dimension$-$often represented by a reference area $A.$ Through the refinement of similarity analysis, derive a functional relationship between a suite of dimensionless variables which governs this phenomenon.