Impulse is the change in momentum of an object. There are two impulses that your egg design will have to deal with. The first impulse is from the drop itself. Its momentum will increase due to the net force applied to it. The next impulse is from the landing. If the egg vehicle doesn't bounce, then the two impulses in magnitude are equal!
Imagine that dropping from a meter, the egg has the whole meter to speed up to its speed right before impact (so the egg doesn't break just from falling because the force is small). At impact, that speed will decrease to zero (as long as it doesn't bounce). But, how much distance does it have when it hits compared to the meter? Not much, which means less time to deal with the same magnitude of impulse.
The basic formula for impulse is F*∆t. Since the impulse is constant, F and ∆t are inversely related to each other. More time means less force...
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