I'm not sure you know how to set up initial parameters at all based on this. The initial velocity between the jumper and the Earth should be 0 m/s, shouldn't it? After all, isn't the jumper at a fixed distance above the Earth, relative to the Earth, when they jump?
While the jumper is on the chair, he would be accelerated at the same rate with the same velocity as the earth and the relative velocity would be zero.
But once he jumps, he is no longer being accelerated. There is no force on him, no acceleration, no velocity. He's just hanging there inert. But the earth is still accelerating while he is hanging there, so the relative velocity between the jumper and the earth would be whatever the velocity the earth is moving relative to the jumper.
This jumper isn't subject to momentum magically somehow? Let's think about this for a second. Let's pretend he's standing on a platform that's, oh, say 30 meters (-ish) above this disc that's accelerating ever upwards at 10m/s/s (-ish, again, for funsies, ok?). The disc has been accelerating for <who the fuck really cares it doesn't matter but let's have fun> 1 hour. The jumper does a trust fall from the platform he was standing on. Once he's in a "free fall" state, after 1 second has transpired, and ignoring air resistance, how fast do you figure that jumper sees the ground approaching him? In other words, what's the relative velocity between the disc and the jumper? Hint: It's not 200000ms.
Edit: Let's ignore the minuscule relativistic effects too, for the sake of ease. Unless you want to try and make the case that it matters somehow in this specific example, in which case I am waited with eager anticipation.