Bungee jumping in Illinois
Great question! Let's look at this one part at a time. First, you asked about the forces on a bungee jumper.
The first force that the bungee jumper experiences is gravity, which pulls down on everything and makes the jumper fall. The gravitational force is almost exactly constant throughout the jump.
During the bungee jumper's fall, he or she also experiences a force due to air resistance. The faster the jumper is falling, the more the air resistance pushes back opposite to the direction of motion through the air.
The third force the jumper experiences is a spring force due to the bungee cord. The amount that the bungee cord pulls back on the jumper depends on how far the cord has been stretched, i.e. the farther the jumper has fallen, the more the cord pulls back on him or her. Below a certain height, the spring force of the bungee cord pulling up on the jumper exceeds the force of gravity pulling down. In that range, even ignoring the air resistance, the fall slows down, and then starts to reverse, so the jumper heads back up.
Now that you know about the forces, let's look at the work that is done on the jumper. Each little bit of work done on the jumper changes their kinetic energy, mv2/2, where m is their mass and v is their velocity. you calculate that work by multiplying the distance traveled times the component of the force in that direction. You can have negative work if the force and direction of motion are opposite to each other.
So now let's look at the first fall that the jumper makes. As the jumper falls down, gravity does positive work because the force of gravity points in the same direction that the jumper falls in. The spring force of the bungee cord, however, does negative work on the jumper because the jumper is falling down while the cord is pulling up. The third force, air resistance, also does negative work during the fall since it pushes upwards. As the jumper reverses direction and starts to spring back up, gravity does negative work because the gravitational force pulls down while the jumper is moving up. The spring force does positive work this time because it is in the same direction as the jumper's motion. However, air resistance still does negative work because now it pushes down on the jumper.