This is a full-scale reproduction of the Jupiter-C launch vehicle built by the Reynolds Metals Company. It has a replica of the Explorer I satellite on top. The Jupiter-C launched the Explorer I on January 31, 1958 as the U.S.'s first artificial satellite.
The Jupiter-C was a modified Army Redstone liquid-fuel rocket with solid-fuel upper stages and a slightly more powerful main stage engine. The Explorer 1 instruments recorded cosmic rays, micrometeorites, temperatures, and radiations. This rocket was transferred to the Smithsonian by the Army in 1959.
This object is not on display at the National Air and Space Museum. It is either on loan or in storage.