Answer.... to see if it was possible for a man to evacuate from a high altitude spy plane and survive....
The SR-71 went to those heights as did the U-2....
We were getting ready to spy on the Ruskies...
This may have been a continuation of the classified "Project Mogul", that was conducted near Roswell, NM in 1947. "Project Mogul" studied the feasibility of using high altitude balloons for surveillance and the possibility of parachuting from great heights. Project Mogul used crash test dummies as test subjects instead of dummies. Because of a few errant balloon flights, and parachute drops, plus the Army Air Corp's reticence about the nature of the sightings by locals, it became the source for Roswell UFO crash legend.
About the same time as the manned experiments, Gary Powers, a CIA pilot, was shot down while flying a U-2 over the Soviet Union. Much to Eisenhower's and CIA Director Dulles' chagrin, Gary Powers survived the crash, was held by the Soviets to publicly humiliate the United States.
Pretty sure the Nazis shot a guy into space on a V-2 rocket actually, but I can't recall many details. The Nazis were working on a winged V-2 to reach New York with an A-bomb.