The air drag force experienced by an airplane in flight, $F_d$, can be represented by the formula $F_d = \frac{1}{2}CpAv^2$, where $C$ is the drag coefficient; $\rho$ is the air density; $A$ is the cross-sectional area of the plane perpendicular to the direction of flight; and $v$ is the speed of the airplane.
If the speed is doubled at a given altitude, what is the resulting increase in the power requirement for the engines.
a. increased by a factor of $\sqrt{2}$
b. increased by a factor of 2
c. increased by a factor of 4
d. increased by a factor of 8