A $2300-$lb car is driven at sea level $(=0\mathrm{.}002378$ slugs$/$ft$3)$ on a level paved surface. The car has CD $=0\mathrm{.}36$ and $24$ ft$2$ of frontal area. The car is designed to achieve a top velocity of $100$ MPH$.$ But when designing the vehicle, an underpower engine was selected because of not account for the aerodynamic and rolling resistance. Assume a $2-$lb weight will be added to each unit of horsepower needed to overcome the additional resistances $($aerodynamic and rolling resistances$).$Find: a$)$ The final weight of the car to achieve the top speed of $100$ MPH$.(10$ pts$)$ b$)$ The distance from the front axle to the center of gravity if the maximum tractive efforts developed from front$-$wheel drive and rear$-$wheel drive are equal. Assuming the wheelbase is $120$ in$,$ and the gravity center is $20$ in above the roadway surface. The roadway adhesion is $0\mathrm{.}6.(10$ pts$)$