I did, in my student days, used the laws of conservation of energy and momentum to work out the conditions for maximum usable energy for a plane flying through air. You get max energy going into propelling the plane when the speed of the exhaust air/gas flow relative to the plane (i.e. the air exhaust going backwards) is twice the speed of the plane going forwards relative to still air.

 

This result is apparently quite general. The simplest is to imagine an impulse water turbine. If the speed of the water jet impinging on the turbine bucket is twice the speed of the bucket receding-- both relative to ground, The end result is that the speed of the water departing from the bucket is zero relative to ground.