Question

How would I start a science project on egg dropping

Answer 1

Find a way to slow down the egg's momentum before it hits the ground.
maybe using a spiral type object to add a subtle spin to slow it down

Answer 2

It actually depends on how you want to go about it. If it was me in your shoes I would do it based on the time it took for the egg to drop. I would use several different type of eggs for my experiment. But first you'll halve to make your prediction, by predicting which egg would drop the fastest or which egg would take a longer amount of time to drop. To make it better you can also do it in several locations.
HOPE THIS HELPS! ^_^