Well, OK — it’s a recreation of about half of Robert Goddard‘s shop, set up at the Roswell Museum and Art Center in Roswell, New Mexico:
After some initial successes, Dr. Goddard moved west to Roswell, New Mexico in 1930. This gave him the room to safely launch rockets, the isolation to allow him to work in near-secrecy, and a dryer climate to help him cope with his history of respiratory ailments. For the next 11 years, he would work with his small team trying to perfect his pioneering liquid-propellant rockets (one of which is also displayed in this image, conveniently cross-sectioned for inspection).
From the placard:
This rocket was built by Dr. Goddard and his crew of three in July of 1938. In the following month, it flew to an altitude of 3,294 feet and dropped slowly back to the prairie by parachute. The height of ascent was measured using a small recording barometer mounted within the rocket.
Although Dr. Goddard continued his pioneering rocketry for another seven years, this was his last successful flight test.
To be specific, the rocket belonged to Goddard’s L series (L-13, to be specific). It burned gasoline and liquid oxygen, and was gyro-stabilized (blast vanes in the exhaust, and air vanes on the fins kept the rocket ascending vertically).