Projectile kinematics

While the vector represents the actual displacement that an object follows, for projectiles it is often useful to think about the path it takes.  That path that a particle takes is called its trajectory.  

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:

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