If my rocket requires thrust $T$ to maintain a velocity $v$, the propulsive power can be calculated using
Assuming the same friction (so the required thrust to maintain the velocity doesn't change) but with double the velocity, I need twice the propulsive power.
I understand the formula but I don't understand the physical reasoning. What does "twice the propulsive power" mean exactly, and why would it need to double to maintain the higher velocity when the resistance to motion (friction) is unchanged?
I understand from wikipedia (https://en.wikipedia.org/wiki/Thrust#Thrust_to_propulsive_power) that a static-fire produces no propulsive power because none of the energy from the thrust goes into moving the rocket, but I don't understand the reasoning here.