Form of the motion of a body launched by an initial velocity along a trajectory determined entirely by gravitational acceleration and air resistance. Neglecting air resistance and rotational effects, a projectile thrown outward into the air follows the path of a parabola. There is no force of horizontal acceleration, only a constant horizontal velocity.

Galileo first discovered that the curved path followed by a projectile is a parabola. He had arrived at his conclusion by realizing that a body undergoing ballistic motion executes, quite independently, the motion of a freely falling body in the vertical direction and inertial motion in the horizontal direction. The effects of air resistance (to say nothing of wind and other more complicated phenomena) are seldom negligible and are necessary for predicting the actual trajectory of a roller coaster.

AT THIS POINT IN THE RIDE . . . the riders experience the sensation of weightlessness as they follow the parabolic path of projectile motion from the point of elevation. The challenge for the roller coaster designer is to design the track so that the shape of the hill approximates the parabolic profile of the coaster in free-fall. On a well-designed ride, the car wheels would have the least possible contact with the track on a descent. To achieve higher rates of speed, the hills must in turn be wider.

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