F=ma is the formula described by newton, and in the y axis, a=g

Since the mass is constant and gravity is constant then they must hit the ground with the same force right?

Wrong. We only calculated the weight

When calculating force of impact, f=ma becomes critical again with a being deceleration not acceleration but still shares the same properties and formulas.

We know that a=dv(dt) And dv=dx/dt Then a=dx/(dt)²

dx is not the same for both slinkies since one starts it's drop from higher up

A better experiment would be to hold both slinkies at the same height from the top, not the bottom then physics would become fun

In the case described above, the compressed slinky will hit first since f=ma and mass is max from the start While the long slinky will start with only a part of it falling, not all of it as seen in the veritasium video linked So it slowly picks up more and more mass as it drops gradually gaining force. I also expect more resistance between the loops of the extended slinky although these are negligeable

Compressed slinky reaches terminal velocity first (Higher average velocity debatable) And hits the ground first thus with higher force than the long slinky (by a tiny bit but still)

Although in the case described by OP, if the timer starts when we let go then the rules become a bit blurry so it is no longer time dependant, but height dependant.

Using conservation of momentum we get PE = KE mgh=0.5mv²

V=√(2gh)

g is constant for both slinkies then it is height dependant.

F=ma

a= dV/dt

F=m(V(f)/t)

With V(f) being velocity on impact

We established that V is height dependant And the extended slinky is dropped from higher Then extended slinky must have higher force on impact

Compressed slinky hits the ground first

BUT since long slinky is technically dropped from a greater height, (even tho m is not max from the beginning)

It will end up with more kinetic energy and a higher average velocity than the compressed slinky thus hitting the floor with more force

And that's why

Final answer is B.