# Energy Trouble

1. Mar 10, 2005

Hi, my professor wants me to solve this problem using energy formulas. I am a little confused on how I am supposed to do this. If anyone wants to give me a lead in the right direction, it would be greatly appreciated. Here is the problem:
"You and a friend charter a small plane to take a tour of the desert. Unfortunately, there are mechanical difficulties during the flight and the pilot is forced to make a crash landing on the top of a mesa that stands 250m above the surrounding plain. The pilot fixes the plane and wants to take off again, but the only reasonably smooth road that could be used for a 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 mph, but the plane needs an airspeed of about 120mph 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 about deliberately driving the plane off the edge and diving downward and forward. By doing this he hopes to pick up enough air speed to pull out of the dive before hitting the ground. Seeing how your life is at stake in this attempt, you decide to do your own calculations.

Thank you

2. Mar 11, 2005

### xanthym

{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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