The energy height, H, of an aircraft of mass m at altitude h and with speed v is defined as its total energy (with the zero of the potential energy taken at ground level) divided by its weight. Thus, the energy height is a quantity with units of length.
a) Derive an expression for the energy height, H, in terms of the quantities m, h, and v.
b) A Boeing 747 jet with mass 3.5 · 105 kg is cruising in level flight at 250.0 m/s at an altitude of 10.0 km. Calculate the value of its energy height.
Note: The energy height is the maximum altitude an aircraft can reach by "zooming" (pulling into a vertical climb without changing the engine thrust). This maneuver is not recommended for a 747, however.
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