Musk's reusable rocket proposition

Revisiting this post.

Thoughts on how a RTLS for a rocket might be done with a limited fuel supply.

Here's a pdf file that shows how to compute a trajectory.  Clearly, the trajectory has to be altered in order for a rocket to return to launch site.

Tentative procedure:

Alter the trajectory upward to act as a brake to forward motion.  That's so you don't go too far out.

Then reverse course when velocity gets slow enough to begin coming back down.  Do another burn in order to get vectored back to launch site.  Then manuever the business end of the rocket toward the ground configuration.  Deploy parachutes and drop down to landing site.  Upon reaching close to ground, start engines and release parachute.  Touch down softly on surface.

Update:

 Here's a graphic that shows a simple rocket trajectory.  Visualize how this could work in practice.

Water rocket appears to mean "bottle rocket" as in fireworks

 
Update:  I hacked the graphic in order to illustrate the proposition.

Hacked graphic to show how it all works: two modes 1) ascending on left 2) descending on right