Q$-2)(30$ P$)$ A $1\mathrm{.}6-$ton automobile that has $2m^2$ of frontal area and $0\mathrm{.}4$ of drag coefficient $(C_D)$ is driven on a surface and the coefficient of rolling friction is $0\mathrm{.}0015$ for all speeds. Assuming minimum theoretical stopping distances, if the vehicle comes to a stop $72m$ after brake application on a level surface and has braking efficiency of $0\mathrm{.}75,$ what is its initial speed a$)$ if aerodynamic resistance is considered and b$)$ if aerodynamic resistance is ignored? $({}_h=1\mathrm{.}04$ and $g=9\mathrm{.}81\frac{m}{s^2})$

If the last digit of your student ID number is even, solve the above question using the following information.

The roadway is wet with good pavement and the automobile is traveling at an elevation of $1500m.$

If the last digit of your student ID number is odd, solve the above question using the following information.

The roadway is dry with poor pavement and the automobile is traveling at an elevation of $3000m.$