A new experimental $2500-$lb car, with C$\_$D $=0\mathrm{.}45$ and A$\_$f $=25$ ft$^2,$ is traveling at $90$ mi$/$h down a $10\%$ grade. The coefficient of road adhesion is $0\mathrm{.}7$ and the air density is $0\mathrm{.}0024$ slugs$/$ft$^3.$ The coefficient of rolling resistance is $0\mathrm{.}0145.$ The braking mass factor is $1\mathrm{.}04.$ The angle of grade is $5\mathrm{.}71$ degrees. The car has an advanced antilock braking system that gives it a braking efficiency of $100\%.$ What is the minimum theoretical stopping distance with aerodynamic resistance? $($K$\_$a $=0\mathrm{.}014)($Report your answer in ft$.)$