Define Rocket in Drag (Princeton)?

A rocket has an effectual frontal area A and blasts off with a constant acceleration a straight up from the surface of the Earth.

a) Use either/or dimensional analysis or an elementary derivation to find out how the atmospheric drag on the rocket should vary as some power(s) of the area A, the rocket velocity v and the atmospheric density p assuming that we are in the region of high Reynolds numbers.

b) Presume that the atmosphere is isothermal with temperature T. Analyzes the variation of the atmospheric density p with height z. Presume that the gravitational acceleration g is a constant and that the density at sea level is P_o.

c) Find the height h_o at which the drag on the rocket is at an utmost.