The rotation of the earth would move the rocket 50 miles iff it was still on the ground.
The rocket, not on the surface, still has that 1000mph extra kick that the earths rotation gave it, but it is above the earths surface and therefore must move faster than 1000mph to keep up with the earth. (Of course it is moving _much_ faster than 1000mph, but the point is that while the rotation of the earth gave it 1000mph, that 1000mph does not keep the rocket above the same position once it is up there).
To understand why you don't maintain the same surface-relative speed as you go up, consider geostationary orbit again (where the numbers are extreme enough to work out intuitively):
Sitting on the launch pad, the geostationary rocket has a "bonus speed" of 1000mph, which is enough to put it stationary over the ground. The surface relative speed, with this 1000mph, is 0, which is your objective for geostationary orbit (~35k kilometers directly above the launch pad).
So all it needs to do is go straight up, right? Wrong. While 1000mph is enough speed to keep up with the earths rotation at sea level, it is nowhere near fast enough to keep up with the earth at ~35k kilometers. It needs to go up ~35k kilometers and it needs to move ~5867 mph faster to the east in order to keep up with the same position on the earth. If you were up at 35k kilometers and moving east at 1000mph, the same speed as the ground is moving at sea level, then the ground would be whipping by you as it rotates underneath you. Plotted on a map, you would appear to be moving very quickly to the west.