find the altitude change of a 10,000 kg fighter which climbs and in doing so loses 100 m/s of airspeed
assuming power output it constant, and air resistance is constant,
mgh=change in KE
mgh=final ke-original ke
mgh=1/2 m (Vf^2-vi^2)
so at this point you are stopped: You are given vf-vi.
mgh=1/2 m ((vi+100m/s)^2-vi^2)
= 1/2 m (200vi+1E4) and that is as far as you can go.
Many of those with a lessor understanding of physics would have done this:
mgh=1/2 m (100^2) then solved, and of course, it would be wrong.