Now that you are familiar with projectile motion trajectories, you may be wondering why the path is always a parabola.
The object follows the path of a parabola, because the only force acting on the object to change it's motion is gravity. Thus, while in the air the object is under the influence of gravity which pulls the skater back down to the earth. There is no force hindering the skater's forward progress. Remember that we are neglecting air resistance because the skaters are not skating all that fast.
The next important step when studying projectile motion is to understand what factors determine the height and length that the object travels. The take-off angle, take-off velocity, and height of take-off are the three factors which determine the figure skater's trajectory during a jump.
When studying projectile motion, it is very important to separate the object's vertical take-off velocity from their horizontal take-off velocity. The reason for this is that gravity immediately starts slowing the skater's vertical velocity when he leaves the ice, but gravity has absolutely no affect on the skater's horizontal motion since it is acting only in the vertical direction. Recall that only an external force acting in the horizontal direction, e.g. air resistance, would affect the skater's horizontal velocity, which we are neglecting.
Once gravity has slowed the skater's upward vertical velocity to zero, gravity then accelerates the skater back to the earth. This is easily shown in a vertical jump. For example, if the skater were to leave the ice with velocity only in the vertical direction (the skater is not jumping forward at all, only up), once he reaches the top of his jump, gravity accelerates him back down.
Notice that when the vertical velocity reaches zero, the skater is always at the top of the jump. This is a very important fact of projectile motion.
The vertical velocity of an object is always zero at the top of the path or at maximum height.