Is it possible to make a "wire-free" Bungee jump? Wireless bungee jump
I think it could be possible with magnets, and the suit of the person has to have a different magnetic camp form the floor camp. But I don't know if the person can rebound.
Is it possible to make a wireless bungee jump?
 A: It would be theoretically possible, but not with magnetic fields [n.b. the word in English is "field"]. The problem with magnets is that they are always dipoles so have a North and South pole. If you jumped with your head a South pole and had South poles on the floor, the slightest imbalance would flip you round and pull you down faster than gravity.
If you want to try it, use an electric field since these can be monopole. Charge yourself up (how much is a tricky calculation, which I don't have time to do). Then charge up the floor to a similar potential (same polarity). You'd need to insulate it well so it doesn't discharge to ground. Also, let's assume the floor is not infinite in extent so that the field diverges a bit (we need this so that the force falls off with height, otherwise you'd accelerate up forever).
When you jump, the repulsion will slow your acceleration and stop you in mid-air. Then you'd float up and oscillate about an equilibrium position until air resistance damped the motion. Eventually, you'd just float there, stationary.
I don't know how you'd get down, though. 
A: 
Wireless bungee jump

It's not a bungee jump without a bungee. You want to simply survive a jump from a normally fatal height.
One problem is the distance over which the deceleration has to take place. If you decelerate from terminal velocity to zero in too a short distance it will require a force greater than that the human body can survive.
The usual method used by stuntmen in pre-CGI films is to have a very large pile of foam and cardboard at the bottom. The also land on their backs to spread the load and avoid compressing their spines etc.
Another method successfully employed is to arrange a landing point in deep snow (tens of meters) on a steep slope.

I think it could be possible with magnets

Magnets tend to work over short distances, You would need a very broad and tall apparatus on the ground.
A: As long as I don't have to actually make it work, and you're willing to jump with a large chunk of steel strapped to your back, a coilgun would seem the way to go. Ordinarily, coilguns are used to accelerate a stationary body to some exit velocity, but there's no reason not to run it in reverse. 
A jumper would fall into the coilgun, and the coils would be activated in sequence to slow her down, then stop her. Rebound, of course, is easily produced, and there's no obvious reason the jumper could not be fired back up to the starting platform.
