If you were in an elevator free-falling 100 floors, and you jumped up, one inch from when the elevator hit the ground, would you be safe?

The normal office building floor is from 2.7 to 3.3 metres.

For your safety let's assume your office is 2.7 metres (this is a floor to floor measurement).
The acceleration of free fall is 9.8 m^2
Your initial V = 0

From the formula V2^2= V1^2+2as (ie final velocity^2 = initial velocity^2 + 2 times the acceleration by the distance.

So V2^2= 0 + 2X9.8X(100*2.7)
V2^2 = 5292
V2 = 72.73 m/s

This is your speed relative to the ground.

The highest standing vertical jump according to Guinness records is 5'3", approximately 1.5748 metres. He would have needed to have an initial speed of 5.556 m\s to reach the top of the pile at which his velocity would be close to zero.

So relative to the enclosed lift when you jump up, you are travelling upwards at 5.556.

Sadly relative to the ground, even at your fastest, you are travelling (72.73 - 5.556), that is,
67m/s towards the ground.

That is a speed of 149.867 mph or 241.2 km/h.

Best of luck.

If the elevator was in a vacuum I think you be accelerating at 32 feet per second squared. But whatever the resistance, still pretty fast. Whether you would survive would likely depend on what cushions, if any, were at the bottom of the shaft. Jumping would make little difference.

er. that second one. your tiny jump just moves you up relative to space in the elevator. you still have 100 floors of falling momentum to overcome.

also in a true free fall, you would perceive yourself weightless in the elevator car.

I don't care how high you jump, you still were falling at the same speed as the elevator

Theoretically, you'd be lifted off the floor and likely suspended in the air. But there would be hardly a free fall because the cabin would be slowed down by the shaft.