Example $3$

The drag coefficient of a car increases when the sunroof is

open, and it requires more power to overcome

aerodynamic drag. The car has a frontal area of $1\mathrm{.}7m^2$;

and the $C_D$ values when the sunroof is closed and open are

$0\mathrm{.}32$ and $0\mathrm{.}41,$ respectively. If the car is moving at a

constant velocity of $55k\frac{m}{h}r,$ determine the additional

power consumption of the car when the sunroof is opened.

Take the density of air to be $1\mathrm{.}2k\frac{g}{m^3}.$

$($a$)$ if the air is calm,

$($b$)$ if wind is blowing against the direction of the motion

of the car at $30k\frac{m}{h}r,$ and

$($c$)$ if wind is blowing in the same direction of motion of

the car at $50k\frac{m}{h}r.$