Consider a subsonic compressible flow in Cartesian coordinates where the velocity potential is given by:

$(x,y)=V_{}x+\frac{70}{\sqrt[\phantom{2}]{1-M_{}^2}}{e}^{-2\sqrt[\phantom{2}]{1-M_{}^2}y}sin2x$

i$.$ Show that the velocity potential given above satisfies the subsonic linearized velocity potential equation.

ii$.$ If the freestream properties are given by $V_{}=700f\frac{t}{s},P_{}=1$atm and $T_{}={519}^{0}R,$ calculate the following properties at the location $(x,y)=(0\mathrm{.}2ft,0\mathrm{.}2ft)$ : $M,p,$ and $T.$