Jet turbines work by sucking in mass of air and ejecting the air backwards.

Lets consider a jet plane flying at constant speed u=500m/s.

In motionless frame of refrence “a” (at rest wrt ambient air) the air, which is initially at rest is sucked in at rate μ kilogram per second and ejected with velocity v. Lets consider case
μ = 200 kg/s,
v=100m/s.

Power of the engine is
Pa = 1/2 μv² = 1 MW

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In the frame of reference “j” of the jet (this frame has airspeed u) the air moving with velocty u = 1000 m/s is sucked at the same rate μ=1000kg/s and ejected with velocity v’= u
+v = 600 m/s, and power is equal to change of kinetic energy:
Pj = 1/2 μ(v’² – u²) = 11 MW.
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So what is real power of the turbine?

I need to know. I am VP enginnering at Lockheed Martin and the government demands now fuel efficient jet planes (boy gas prices hurt, do not they) and the engineers around here are no use. Please help us.
Sorry my secretary messed up again.
Should be
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In the frame of reference “j” of the jet (this frame has airspeed u) the air moving with velocty u = 500 m/s is sucked at the same rate μ=200kg/s and ejected with velocity