Marx called these "Long Range Rockets with Launching Pads" in the write-up for the 1961 Sears Wishbook, but I'm not sure what prototype rockets/missiles these were meant to represent.
The hard plastic launching pads came in three pieces - two hard plastic launch pad pieces and one spring which is missing from my launchers - and were usually color-matched (I switched the colors around for the photos to provide a bit more contrast). The Ajax style rockets had a hard plastic 1st stage and a soft plastic 2nd stage with a set being one launcher and three 2-stage rockets. There appears to be three different types of rockets - that is, three different second stages (I only have two variations in my collection). Eventually, all components were molded in a variety of colors, but early sets tended to have all white launchers. The launch base is 2.5" (6.35cm) diameter base. Overall, the height with launch pad is: 6.5" (16.51cm) (Rocket #1) and 7" (17.78cm) (Rocket #2).
Ed
The yellow HP launch pad on the far right has perhaps shrunk with age and won't allow me to push the rocket down all the way, and I don't want to force it and risk breaking it.
NOTE: all my launchers are missing their springs.
Two different 2nd stages are shown here.
There were three different castings for the 2nd stage pictured at far right. I only have two. From looking at catalog pages, the third casting appears to have additional little nubs at the very top.