If you drop a raw egg on the ground, it will break. If you drop it on a saggy sheet, it does not. Explain in terms of momentum and/or impulse.

force is change of momentum / time to change it

if the target is soft, it takes longer to change the momentum
so the force is less

or

work done = change in kinetic energy = force times distance
to get the - (1/2) m v^2 needed, we can use a big force over a short distance or a small force over a great distance. The soft target provides a greater stopping distance so less force.
(LOL, they did not ask for an energy argument though)

When a raw egg is dropped, it will break upon impact with the ground due to the sudden change in momentum. To understand why dropping it on a saggy sheet prevents it from breaking, we can consider the concepts of momentum and impulse.

Momentum can be defined as the product of an object's mass and its velocity. It is a vector quantity, meaning it has both magnitude and direction. When the raw egg falls and hits the ground, its momentum changes abruptly, since the velocity suddenly shifts from moving downwards to coming to a halt. This sudden change in momentum results in a large force being exerted on the egg, causing it to break.

On the other hand, when the egg is dropped onto a saggy sheet, the sheet absorbs some of the egg's momentum. As the egg hits the sheet, the sheet begins to deform, temporarily increasing the contact time between the egg and the sheet. By extending the time over which the momentum change occurs, the force applied to the egg decreases, reducing the likelihood of it breaking.

Therefore, the saggy sheet acts as a cushion, extending the impact time and reducing the force exerted on the fragile raw egg. This increased contact time reduces the impulse (change in momentum) experienced by the egg, making it less likely to break.