Example 8 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 ft/sec², and the downward acceleration component is the acceleration due to gravity at that altitude, which is g=30 ft/sec². At the instant represented, the velocity of the mass center G of the rocket along the 15° direction of its trajectory is 12,000 mi/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 B. 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. Horiz. G 20 ft/sec² 15° v = 12,000 mi/hr P n g = 30 ft/sec²