A $2300-$lb car is driven at sea level $(\backslash$rho $=0\mathrm{.}002378$ 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 $0\mathrm{.}6.$