Designing a Physics Project: "Scrambler

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MajikWaffle
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Our physics class is going to be doing a project soon called the "Scrambler", and I have no clue where to start from. Our teacher never explained designs with us.

The rules are that each contestant will design and build a system that will transport a Grade A uncooked large chicken egg (5.0 - 15.0 cm above the ground) a distance between 8.000 - 12.000 meters as fast as possible without leaving a 2m wide lane.

The system consists of two parts, the egg transport subsystem and the energy propulsion subsystem. These subsystems may be separate or combined into a single unit. And the source of energy will only come from a 1.000 kg mass in freefall. Also, we can't use any excessive accesories such as electronics or springs.

The performance value is going to be calculated by 3 times the run time plus stopping distance.
Performance = [3 * Run Time (seconds) + Stopping Distance (cm)]

As I said, I have a limited idea of what to do and what parts to use. As far as I know of, a pulley system would be good. Any designs or links to designs to get me started would be greatly appreciated.
 
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You lost me on that one, Alkatran. How in the world would you put a gravity-operated slingshot into action?
 
Yeah, we can't use slingshots because that's elastic. We could do trebouches (sp?) but that's really hard.