(Solved): 10. As part of their training, astronauts (used to?) ride the "vomit comet", NASA's reduced gravity ...

10. As part of their training, astronauts (used to?) ride the "vomit comet", NASA's reduced gravity KC 135 A aircraft that performs parabolic flights to simulate weightlessness. The plane starts at an altitude of 20,000 feet and makes a steep climb at 52 degrees with the horizon for 20-25 seconds and then dives at that same angle back down, repeatedly. The equation governing the altitude of the flight above the ground is \[ A(x)=-0.0003 x^{2}+9.3 x-46,075 \] where \( A(x) \) is the altitude and \( x \) is horizontal distance in feet. a) What is the maximum altitude the plane attains? b) Over what horizontal distance is the entire maneuver performed? (Remember the starting and ending altitude is 20,000 feet.)