A ski jumper's energy is equal to Potential Energy and Kenetic Energy. The basic ski jumping equation without the force of friction or air resistance being considered is:

Total Energy = Mass of Skier * Force of Gravity * Height + 0.5 * Mass * Velocity^2

At the top of the hill, all of the skiers energy is potential energy. During take-off, potential energy turns into kenetic energy so that both potential and kenetic energy are equal.

When the ski jumper becomes air-borne, he is subject to the force of gravity and the different forces moving through the air. To get the maximum distance, the ski jumper must maximize lift and minimize drag. The most ideal way of doing this is by spreading the skis into a v-shape, which gives the skier the most surface area and increases lift. The tails of the skis are crossed in order to minimize drag.

The ski jump itself is shaped like a parabola. This parabola almost matches the general path of the ski jumper. This also makes so the skis are never more than 3-5 meters above the ground.

SOURCE:

Cull, Thomas. What Are The Physics Behind Ski Jumping?. 1998. 20 Nov. 2004