Projectile kinematics

Projectile kinematics is the study of kinematics of projectile bodies. Projectile bodies follow a path, called a trajectory. Generally, projectile kinematics is a form of two-dimensional motion, with a vertical velocity vector, which changes with respect to the acceleration due to gravity, and a horizontal velocity vector, which does not have an acceleration exerted upon it.  

Range

The range of a projectile system represents the farthest possible distance that it might travel.  The range $R$ is inversely proportional to the product of the initial velocity $v_0$ and angle of release $\theta$, and acceleration due to gravity $g$, such that:

$$R=\frac{v_0^2\sin (2\theta )}{g}$$