The two major forces opposing the motion of a vehicle

moving on a level road are the rolling resistance of the tires,

F$"$ and the aerodynamic drag force of the air flowing around

the vehicle, Fd$,$ given respectively by

F$,=$ f$\backslash$deg W$,$

where f and Cd are constants known as the rolling resistance

coefficient and drag coefficient, respectively, $\backslash$deg W and A are

the vehicle weight and projected frontal area, respectively, V

is the vehicle velocity, and p is the air density. For a passenger

car with $\backslash$deg W $=3550$ lbf$,$ A $=23\mathrm{.}3$ ft$2,$ and Cd $=0\mathrm{.}34,$ and

when f $=0\mathrm{.}02$ and p $=0\mathrm{.}08$ lb$/$ft$3$

$($a$)$ determine the power required, in hp$,$ to overcome rolling

resistance and aerodynamic drag when V is $55$ mi$/$h$.$

$($b$)$ plot versus vehicle velocity ranging from O to $75$ mi$/$h

$($i$)$ the power to overcome rolling resistance, $($ii$)$ the power

to overcome aerodynamic drag, and $($iii$)$ the total power, all

in hp$.$

What implication for vehicle fuel economy can be deduced

from the results of part $($b$)$

$2\mathrm{.}22$ The two major forces opposing the motion of a vehicle moving on a level road are the rolling resistance of the tires, $F^{\text{'}\text{'}}$ and the aerodynamic drag force of the air flowing around the vehide, $Fd,$ given respectively by

$F_s=fW,F_d=C_d{A}_{2P}^1{V}^2$

where $f$ and $Cd$ are constants known as the rolling resistance coefficient and drag coefficient, respectively, $W$ and A are the vehicle weight and projected frontal area, respectively, $V$ is the vehicle velocity, and $p$ is the air density. For a passenger car with $W=3550lbf,A=23\mathrm{.}3f{t}^2,$ and $Cd=0\mathrm{.}34,$ and when $f=0\mathrm{.}02$ and $p=0\mathrm{.}081\frac{b}{t}{a}^3$

$($a$)$ determine the power required, in hp$,$ to overcome rolling resistance and aerodynamic drag when $V$ is $55m\frac{i}{h}.$

$($b$)$ plot versus vehicle velocity ranging from $O$ to $75$mih $($i$)$ the power to overcome rolling resistance, $($ii$)$ the power to overcome aerodynamic drag and $($iii$)$ the total power, all in hp$.$

What implication for vehicle fuel economy can be deduced from the results of part $(b)?$