A certain rocket maintains a horizontal attitude of its axis during the powered phase of its flight at high altitude. The thrust imparts a horizontal component of acceleration of \(20 \mathrm{ft} / \mathrm{sec}^{2}\), and the downward acceleration component is the acceleration due to gravity at that altitude, which is \(g=30 \mathrm{ft} / \mathrm{sec}^{2}\). At the instant represented, the velocity of the mass center \(G\) of the rocket along the \(15^{\circ}\) direction of its trajectory is \(12,000 \mathrm{mi} / \mathrm{hr}\). For this position determine \((a)\) the radius of curvature of the flight trajectory,

(b) the rate at which the speed \(v\) is increasing,

(c) the angular rate \(\dot{\beta}\) of the radial line from \(G\) to the center of curvature \(C\), and \((d)\) the vector expression for the total acceleration a of the rocket.

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Horiz. C 20 ft/sec 15" 12,000 mi/hr g= 30 ft/sec