From the conservation of energy, the total mechanical energy is given by the sum of the kinetic energy and the potential energy:

$$$\overline{){{\mathbf{E}}}_{\mathbf{m}\mathbf{e}\mathbf{c}\mathbf{h}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}{\mathbf{+}}{\mathbf{m}}{\mathbf{g}}{\mathbf{h}}}$

Suppose a 1.6x10^{5}-kg airplane has engines that produce 125 MW of power.

Part (a). How many seconds would it take the airplane to reach a speed of 265 m/s and an altitude of 13.5 km, if air resistance were negligible?

Part (b). How much power did the plane use, in megawatts, if this process actually took 825 s?

Part (c) Using the power consumption from papart (b), what would be the magnitude of the average force, in newtons, of the air resistance, if the airplane took 1050 s and traveled in a straight line at a constant acceleration to the specified altitude?

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