A pilot makes a crash landing on the top of a mesa that stands 250 m above the s

Question

A pilot makes a crash landing on the top of a mesa that stands 250 m above the surrounding plain (a mesa is a hill with very steep sides and a flat top). The pilot fixes the plane and wants to take off again, but the only reasonably smooth road that could be used for the runway is not long enough: the pilot estimates that the maximum speed the plane is likely to reach before going off the edge of the mesa is about 45 mi/h, but the plane needs an airspeed of about 120 mi/h before the wing's lift becomes significantly larger than the plane's weight.

Noting that the side of the mesa is essentially a vertical cliff, the pilot thinks that by deliberately driving the plane off the edge at 45 mi/h and diving downward as well as forward, the pilot might cause the plane to pick up enough airspeed to pull out of the dive before hitting the ground.


What would you advise the pilot to do: try it, or hope for rescue (and risk dying of exposure and dehydration)?
(Do not ignore either the lift or drag interactions between the plane and the air, but do remember that the plane also has a propeller.)

Explanation / Answer

{Mass of Airplane & Contents} = M {Kinetic Energy Required for Flight} = (1/2)M(120 mph)^2 = = (1/2)M(53.6448 m/sec)^2 = (1439)M {Kinetic Energy Available from Runway Takeoff} = (1/2)M(45 mph)^2 = = (1/2)M(20.1168 m/sec)^2 = (202.3)M {Additional Kinetic Energy Required from Cliff Drop for Flight} = (1439)M - (202.3)M = (1237)M {Potential Energy Available from Cliff Drop} = M*g*h = M(9.8)(250 m) = (2450)M Since available Potential Energy exceeds additional Kinetic Energy required for flight: Pilot's Plan Is Predicted To Be Successful.

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