Assume the motion of the projectile is being measured from a free fall frame which happens to be at (x, y) = (0,0) at t = 0. The equation of motion of the projectile in this frame (by the equivalence principle) would be y = x tan ⁡ ⁡ ( θ θ ) . The co-ordinates of this free-fall frame, with respect to our inertial frame would be y = − − g t 2 / 2 . That is, y = − − g ( x / v h ) 2 / 2 .