Egg Drop Project: How to Make it Work?

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The egg drop project requires a raw grade "A" egg to be protected in a device no larger than 2.75 inches on each side, while ensuring it stays airborne for at least six seconds during a drop from 5 to 5.5 meters. Suggestions include using a large black trash bag as a parachute, cutting it into a circle, and attaching strings for stability. It's recommended to experiment with different designs and consider cutting a hole in the parachute for better airflow. Using tape to secure the strings to the parachute is also advised. Creativity and experimentation are key to successfully completing the project.
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Ok here's the thing: I have the classic egg drop project, but am not sure how to get it to work, so here are the requirements/details:
The egg is a gresh, raw, grade "A" egg,
Egg cannot be completely encased within another material besides a zip-lock bag.
Device the egg is in can't exceed the dimensions of 2.75 in x 2.75 in x 2.75 in.
Egg/parachute must stay in the air for at least 6 seconds, and land completely intact on the ground.
The height of the drop is 5 - 5 1/2 meters.
It must have some kind of parachute, and something to hold the egg.
P.S. Please help me soon, because it is due w/in the next week, but I really need some help with ideas and most of the work done w/in the next 2 days.
I originally thought a plastic bag would make a good parachute, but it was not airborne long enough. Any ideas would be appreciated.
 
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For a parachute, use one of those huge black trash bags.

Cut a nearly perfect circle in it and then attach something like... 8 strings on the ends...
 
The trash bag idea, how are u supposed to attach the bag to it; do u mean on the outside of it or the inside of the parachute?
 
You have to try a few things out, physics=cool, that's really the idea of this sort of thing. It's fun. And it's fun looking up what other people have done and seeing if you can do better. PS: If you end up with a parachute try cutting a modest hole in the centre, it makes it nice and stable. PPS: Try cellotape for attaching your thread to the plastic.

http://www.google.co.uk/search?hl=en&q="egg+drop+project"&meta=
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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