Meriam, Kraige & Bolton — Kinetics of Systems of Particles: Problem 4_55

4/55 The VTOL (vertical takeoff and landing) military aircraft is capable of rising vertically under the action of its jet exhaust, which can be “vectored” from \(\theta \cong 0\) for takeoff and hovering to \(\theta = 90^\circ\) for forward flight. The loaded aircraft has a mass of 8600 kg. At full takeoff power, its turbofan engine consumes air at the rate of 90 kg/s and has an air–fuel ratio of 18. Exhaust-gas velocity is 1020 m/s with essentially atmospheric pressure across the exhaust nozzles. Air with a density of 1.206 kg/m³ is sucked into the intake scoops at a pressure of −2 kPa (gage) over the total inlet area of 1.10 m². Determine the angle \(\theta\) for vertical takeoff and the corresponding vertical acceleration \(a_y\) of the aircraft.