Two-Stage Balloon Rocket - Take One

I saw this experiment sketched out on a sample page from The Critical Thinking Co.'s Developing Critical Thinking through Science, Hands on Physical Science workbook.  It's basically just the traditional balloon rocket, with the twist of a second balloon added, to simulate a two part rocket.

We're working through a wind power science kit, and I thought, being air powered, the experiment might fit in nicely as a quick "wow" type project, before bed.

We started out with a couple of balloons, a Styrofoam cup, a straw, a ball of string, tape, and scissors.

Following the Critical Thinking Co.'s instructions, we cut the cup in half, and discarded the bottom half.

Then, we cut two short pieces from the straw...

...and threaded them onto the string, making sure they could slide freely, up and down the string.

We blew one of the balloons up, and pulled the untied neck through the cup, pinching it to keep the air in the balloon.

Then, we placed the second balloon into the cup, from the other side..

...and blew it up, until it was large enough to hold the neck of the first balloon in place (easier said than done).

We taped the straws to the balloons.  I probably should have mentioned to the children that they needed to be in a straight line, before I told them to quickly tape the straws on.

Once we got the straws straightened out, I handed off the camera (meaning, get ready for some very blurry shots), and had one of the children hold the end of the string on the side of the first balloon, as high in the air as they could, while another of the children held the other end of the string, tight to the floor, as I...

...prepared to let go of the second balloon.  The idea was for it to propel the rocket a little way up the string, and as it deflated, release the neck of the first balloon, which in turn would let out its air, propelling the rocket even farther up the string.

Unfortunately, the second balloon was deflated before I could even pull my hand away, and the front balloon emptied nearly as fast...

...the straws didn't move on the string at all.  All that really happened was that as the balloons got smaller, the cup slipped down over them, and fell off the bottom of the string.  Not quite the "wow" I was going for.

It was getting late though, so I sent the children off to bed, mulling over the problem of our failed project.  Hopefully, they wake up fresh in the morning, with ideas for improving our second attempt.