What is meant by 'terminal velocity' for a skydiver, and what forces are acting when a skydiver is falling at terminal velocity?
There are effectively two forces acting: gravity and air resistance. Gravity is easy:
When a parachutist first leaves the plane, with the chute not open, the main force acting is gravity. As her speed through the air increases, the air resistance also increases. At 'terminal velocity', which is about 200 km/h, the air resistance force balances the gravitational force and the parachutist stops accelerating and falls at constant velocity.
Once the parachute is open the air resistance is much greater due to the greater surface area, so the new new 'terminal velocity' is much slower, perhaps 20 km/h or so. The forces will again come into balance (when the chute first opens there is a net upward force which slows the downward motion) and the parachutist will fall at the slower velocity.
Actually calculating the value of the air resistance force is easy at either of the terminal velocities, since it is just the same in an upward direction as the gravitational force in the downward direction. It is very hard during any of the accelerations, because it requires understanding the shape of what is falling, the density of air and a number of other variables, and requires fairly sophisticated calculus.