In the movie, \"Superman Returns\", there is a scene where superman stops a malf

Question

In the movie, "Superman Returns", there is a scene where superman stops a malfunctioning airplane while flying in the air and forces the plane to gently land on a football field. Assume that Superman uses a kind of fuel in his body (chemical or nuclear) and via the emission of gases or a mysterious radiation, he can stop the plane and make it land smoothly. Make a Fermi calculation and estimate the energy that superman should consume in order to accomplish the feat.

Hint to answer the previous question: The energy that superman should spend should be equal to the initial total energy of the plane (kinetic? + gravitational potential?) Assume that the plane is a Jumbo 747 full of passengers and it flies at the maximum height with its maximum speed. Use the data below to estimate the total mass, kinetic and potential energy. Now you have an estimate of the total energy that Superman should spend in order to stop and bring the plane gently to the ground.

(BOEING 747-400 SPECIFICATIONS Wingspan: 211 ft. 4 in. Length: 231 ft. 10 in. Height: 63 ft. 8 in. Empty Weight: 403,500 lbs Gross Weight: 875,000 lbs Top Speed: 628 mph Service Ceiling: 45,000 ft. Range: 8,380 miles Engine/Thrust: Four General Electric CF6-80s/44,700 lbs each Crew: 2 pilots, as many as 20 or more flight attendants Passengers: 568)

Explanation / Answer

the total energy superman has to spend is E
E = KE of the plane + PE of the plane
now, mass of Jumbo 747 with passengers and payload, m = 333,400 kg apx
flying altitude of the plane, h = 11887.2 m
cruise speed of jumbo 747 = 0.8 mach = 0.8*343 = 274.4 m/s
hence
E = 0.5mv^2 + mgh = (0.5*274.4^2 + 9.81*11887.2)333,400 = 51430654740.8 J

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