The purpose of this assignment is to practice deriving, and using, the general equations of motion for an aircraft. 1. Derive the equations of motion for the Boeing 747 using an orthogonal set of coordinates that are aligned with the horizontal and vertical axes. 2. Derive the equations of motion for the Boeing 747 using an orthogonal set of coordinates that are aligned with the chord of the wing. 3. Assuming all forces act through the center of mass of the airplane (at the location shown in the gure), derive the summation of moments equation about the nose of the airplane. 4. For a 747 cruising at M0508 and at 30,000 ft of altitude, how much power are the engines producing to maintain steady, level ight? a) How many AA batteries would you need to replace the 4 engines? b) How much do all of those batteries weigh as compared with the 4 engines? 5. Repeat questions (1) (3) without assuming accelerations = 0. Solve for the accelerations of the 747. Make any needed additional assumptions that are required to solve this problem.