Question
One of the methods used to train astronauts for the effects of "zero gravity" in space is to put them in a especially equipped plane that has been stripped of seats and fitted with padded walls. The pilot after that takes the plane up to an altitude of typically 9500 meters and, at a speed of 800 km/hr, puts it into a sudden steep climb. He then pilots the plane so that it follows parabolic trajectory of free fall until it is falling at the utmost allowable rate for safety. He can do this by flying the plane so that he is in continuous free fall himself. (He is trained to do this.) If the greatest angle of elevation that can be achieved in his initial rise is 21.5 degrees and likewise the highest angle of descent for safety is 21.5 degrees, how long (in seconds) will the astronaut trainees experience zero gravity?