H2P I think you've kind of missed the point, although its good to see you concede a bit to momentum.
By teleporting to the opposite side of the earth instead of shooting down toward the earth, you would shoot up into the sky (Force acts in vectors, say if it's midday on the side you telported from, it would be midnight on the opposite side and you would be moving relative to the sun if you want to think in vectors, not relative to the Earth's gravitational pull). Gravity would then use it's force upon your mass, pulling in the opposite direction to your current momentum, eventually reducing your velocity to zero and you having no momentum at which point it would be safe to teleport to terra firma before you start speeding up again.
Its like throwing a ball straight up, at a certain point it stops completely before beginning to descend.
The math would actually be extremely simple, velocities, forces and Earth's gravity are the first things they teach you when dealing with physics.
All this ignores wind resistance etc.
Say the jumper weighs 75kgs (165 lb).
Earth's gravity acts with an accelleration of 9.2m/s^2
so the force acting upon him is
F= 75 * 9.2 = 690N (Newton's)
No matter where on earth he is.
Momentum = Mass * Velocity
Say he's fallen for 10 seconds
Acceleration = (Vf - Vi)/t
Look, I could keep going on about this, but essentially, this is alot easier: If he fell for 10 seconds, in order to cancel his momentum he would need the same force acting upon him in the opposite direction for the same amount of time. God why didn't I think of that earlier, I'm not deleting those calculations though, so if you would like to keep working on them for no reason at all, go for your life. If he were to jump starigh to terra firma, a force in the opposite direction would have to be massively greater in order to compensate for the much shorter "falling" time, probably about 0.2 seconds worth, so the force acting directly on his body would be 50 times greater.
If you're looking in a signature for some astonishing insight into the way things are, keep on lookin'.