In a two dimension projection of a projectile in to the air, from ground at an angle Ф with the horizontal and initial speed of u, the projectile follows a path.
let the origin be the point of projection. x axis is parallel to the ground. y axis is perpendicular to it.
x = u cosФ t
=> t = x / (u cosФ)
y = u sinФ t - 1/2 g t² using the equations of motion.
= u sinФ * x /(u cosФ) - 1/2 * g * x² / (u² cos² Ф)
y = x tan Ф - g x² / (2 u² cos² Ф)
this is called as the projectile equation, which relates x with y coordinates of the projectile at any time t.