Thread: What am I missing?

Hello everyone,
I have a "thought experiment" that I cannot seem to figure out, and would love it if someone could explain it:


Imagine two rockets, both of the same weight, are shot up from the surface of the earth. Both are accelerating at 320 feet/sec/sec. One accelerates for one second before cutting its engines, and the other accelerates for two seconds before cutting its engines. Assume for this thought experiment that there is no atmosphere or friction from wind, that the amount of mass lost from from each rocket from the burning of fuel is negligible, that the earth's gravitational pull is the same at the different altitudes, and things like Special Relativity and solar winds have no effect. In this example then, as I understand it, the second rocket would shoot up four times higher than the first rocket, resulting in four times the potential energy when it reaches its highest point, than the first rocket, and yet only expend twice of the amount of energy (fuel) to do so. What am I missing here?

Originally Posted by Wundergeist

only expend twice of the amount of energy (fuel) to do so.

Where are you getting this from? That is a clue, BTW.

I am assuming (perhaps incorrectly) that the second rocket would use twice as much fuel based on the equation F=MA, or force equals mass times acceleration. If the acceleration of both rockets is constant, and if their masses are both the same, then the amount of fuel being expended by both rockets is exactly the same at any given point in time. If true, then the rocket firing its engines twice as long would expend twice the amount of fuel.

Ok, Work = Force x ?