Physics of Skydiving

Drag

When Joe jumps from the airplane, both gravity and air resistance (a type of frictional force) immediately begin to act on his mass. While gravity remains constant, air resistance does not. Air resistance will increase as Joe's earthbound velocity also increases.

(http://www.physicsclassroom.com/Class/newtlaws/u2l3e.html)
As you can see, air resistance does increase as Joe continues his free fall.

The force of the air particles colliding into Joe's body can be altered even further. Joe can change the shape of his body, increasing:

(http://www.photosport.com/skydiving/tand0143.jpg)
The spread eagle position (mostly horizontal)

(http://www.drstolz.com/Images/Judy-Skydiving.jpg)
A vertical position

or decreasing his cross-sectional area. This change can increase or decrease Joe's velocity.

The amount of drag (resistant) force exerted on Joe's body can be represented by the following equation:

R = .5 * D* p * A * v^2

Where D is the drag coefficient, p is the density of the medium, in this case air, A is the cross-sectional area of the object, and v is velocity of the object. As you can see, if velocity or cross-sectional area is increased, the drag force will also increase. Eventually the drag force acting on Joe will equal the force of gravity. At this point Joe will have a net force of 0 N acting on him, thus he has reached his terminal (max) velocity (which is discussed on another page on this site).

Despite that Joe is no longer accelerating, it is apparent that he is still traveling at an incredibly high rate of speed. In order for Joe to land safely on the earth, he will have to slow down significantly. In order to accomplish this feet, Joe increases his cross-sectional area through the use of a parachute. This increase in the cross-sectional area will cause an extra upward force, so Joe will begin to accelerate in the upward direction, also known as deceleration.

(http://wings.avkids.com/Book/Sports/Images/parachute.gif)
As you can see, the cross-sectional area of the parachute is much greater than that of Joe. Also note the top vent on the parachute. This is prevents the shoot from crumpling up and folding upwards, as air attempts to flow via means of least resistance.
Since an increase in cross-sectional area also causes a decrease in Joe's velocity, eventually the forces will equilibrate, and Joe will cease to accelerate. When this finally occurs, Joe's rate of speed should be relatively low, allowing him to land safely on the earth.

Here is a full summary of the change in force of the process:

(http://www.physicsclassroom.com/mmedia/newtlaws/sd.html)