This Demonstration shows the trajectory of a rifle bullet determined as a function of bullet characteristics and settings of the telescopic sight of the rifle.

The equations describing the bullet trajectory are:

,

,

,

,

with initial conditions

,

,

,

.

Here

is time,

and are the horizontal and vertical dimensions,

and represent the horizontal and vertical velocities,

is the initial rifle bore angle,

stands for the overall drag coefficient due to air resistance,

is the force of gravity, and

is the height of the telescopic sight above the rifle bore.

These equations are solved using the built-in Mathematica function NDSolveValue. The result shows the bullet trajectory and bullet impact in a target at 100 yards for different settings of the telescopic sight. Published bullet velocities at the muzzle and at 100 yards are used to determine the overall drag coefficient . The solutions of this simple model agree closely with published ballistic tables obtained with advanced professional ballistic models [1].