Two complicated true-false questions addressing impulse-momentum misconceptions

Toward the end of the impulse-momentum unit, after my class has played conceptually and experimentally with the impulse-momentum theorem, I ask the following on a daily quiz:

1. True or false: Two identical-mass object that fall from the same height must experience the same force during the collision with the ground.

2. True or false: Two identical-mass objects that each collide with the ground for the same amount of time must experience the same force in the collision. 

These require complex reasoning, at the absolute limit of what I expect from conceptual students after building skills for most of the year; and dead-center of the reasoning level expected from AP Physics 1 or C students.

I'm addressing misconceptions involving the impulse-momentum theorem.  In particular, students invariably look at J=Ft and assume that the force involved is just the weight of the object.  No!  When an object hits the ground, F is the force of the ground on the object, which generally bears no relation to the weight.

What are the answers:

For 1, imagine that one object hits muddy ground, the other hits concrete.  Not the same force.  (From J=Ft, J is the same for both, but t is bigger for mud, so F is bigger for concrete.)  So false.

For 2, same time of collision doesn't mean same impulse, i.e. momentum change!  For example, consider a happy and sad ball.  One bounces, one sticks - but time of collision is about the same for both.  Or, one egg that splats on concrete from a high height, one egg that hits on concrete from a lower height.  About the same time of collision, but the egg dropped from higher height changes its momentum by more, so experiences a bigger force. Also false.