The problem however that after a few launches the bottle tends to crack and actually can explode. So how do you make a tail that is removable and does the trick and can be used multiple times?
Cut 2 pieces of one inch 22mm pvc pipe. Cut the neck of a bottle clean off the bottle next to the collar. Get about 30 cm (a foot) of 20 mm pvc pipe and a bottlecap.
Glue one part of the 22 mm pipe to the 20 mm pvc pipe and glue the neck of the bottle over the 22 mm part (see photo).
Heat one end of a 22 mm pvc pipe and push the end in the table so that the edge bends outwards (the pipe starts to look like an old fashioned top-hat that Abe Lincoln seemed to favor).
The top-hat fits in a bottleneck. With a rubber O-ring it should be able to seal the opening, the 20 mm pipe goes into the bottom of the top-hat..
Cut the bottlecap in the usual way (just like a nozzle cap)
Now glue the top-hat part to the 20 mm pipe... The bottle cap gets locked in... so don’t forget to shove that over the 20 mm pipe...
Assemble the rocket by screwing the cap tight... It pulls the top-hat into the bottleneck
This is it... make some fins and stick these to the end of the pipe, put on a regular rocket nozzle and you are good to launch...
Have Fun!