Newton's Second Law and Motion
The Boeing 767 Problem

The long-range Boeing 767 wide body jet first flew in September 1981.  It is a twin-engine jet that carries up to 290 passengers.  The advantage of this jet to major airlines is that it uses 30% less fuel than comparable jets, and its takeoff performance allows airlines to serve the heavily traveled domestic routes.  An added benefit related to its fuel savings is that it is capable of longer non-stop flights, such as those across the Atlantic and Pacific Oceans.  Its range is approximately 11400 km, a distance one-fourth around the world.

The jet is built with a maximum take-off weight of 186,000 kg, including the fuel capacity of 91000 L (24000 gal), equivalent to 64000 kg.  It's maximum cruising speed is 266 m/s (0.80 Mach) at 11,000 m (35,000 ft). The minimum take-off speed (Vr) is 200 km/hr.  The 767 is powered by two Rolls Royce RB211-514G/H jet engines.   Each engine has a thrust of 270,000 N.  The coefficient of rolling friction is 0.016.

Last year on the fully loaded American Airlines Flight 569 out of Miami International over the Atlantic Ocean, Captain Ray Action noticed a low-fuel indicator light.  Fearing for his passengers' safety, an emergency landing was arranged on a small island near Bermuda.  Captain Action set the jet down on a runway with a length of 610 m.

The problem was traced to a faulty low-fuel indicator light.  The jet, in fact, had plenty of fuel to continue its journey.  Captain Action was now faced with the decision to take off from this runway with the \$110 million jet.  He sought out anyone on the jet who had physics and asked you to share in the decision of whether to take off or not.

Given the above information, calculate and prove your decision for Captain Action.  Make any suggestions that will allow the jet to safely get back into the air.  Show all work and units.

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