You can have members pair up or work individually depending on the amount of members, or what the group whats to do.
Have members create devices that will cushion the egg when dropped from a certain height. Remind the members when they are making their project, to make sure they can take the egg out easily, so you can see if it cracked or not,
Give them a set time, 45 minutes should be plenty of time.
After they are all done, put the egg inside their project and drop them all from a set height.
The goal is to make sure that no eggs crack or break.
Science Behind It
The idea is the materials will cushion the egg and prevent it from breaking. The higher the height of the drop the more cushion the egg will need because the acceleration will be higher meaning the impact will have more force. Acceleration is how many meters (or any distance) per second and object speeds up. Force is how much one object is pushing on another object. For example, we all exert a force on the earth (this is the gravitational force) and the Earth pushes back on us ( this is the normal force; it also prevents us from being crushed by gravity). The acceleration equation is A=d/s^2 and the force equation relating to acceleration is F= mA. These equations show that if you increase your drop height, your acceleration will increase, which will also increase the force. The equation F= mA is also Newton's 2nd Law of Motion. For more information about Newton's Laws of Motion, please refer here https://www.khanacademy.org/science/physics/forces-newtons-laws.
Tips
Have an adult leader drop the eggs to make sure no members get hurt. Also you can encourage members to bring materials that they would want to use.