A classic example of a projectile motion problem is calculation of the ballistic trajectory of a projectile under gravity. This problem illustrates the basic form of projectile motion problems and is illustrated in a number of simulation games that provide an intuitive way to examine the problem and its solution.
Calculation of a projectile's ballistic trajectory involves determining the path of the projectile from an initial point and velocity under the influence of gravity, while ignoring all other forces. In the context of an artillery simulation game, the objective is usually to calculate the proper trajectory and velocity to make the projectile land on a particular target. Assuming the projectile is launched across a flat surface, the projectile's impact point can be determined by multiplying the square of the initial velocity by the sine of the launch angle multiplied by 2, then dividing that quantity by the value of the acceleration due to gravity. More complex versions of the ballistic trajectory problem often encountered in simulators and in real application involve the application of aerodynamic drag forces, winds and acceleration by the projectile after the initial launch. In some cases, the desired point of impact may not be at the same altitude as the point of launch, further complicating the calculations of the proper launch angle and speed.