The parabolic motion is the union of two simultaneous and independent straight motions, one uniform and one constantly accelerated.
Projectile motion with initial velocity and an angle θ
In this case the projectile is constantly accelerated by the gravitational acceleration along the y axis, on the other axis the motion is uniform as there are no forces or accelerations.
SCOMPOSITION OF MOTION:
We obtain from  and we replace it in  to find :
We impose in order to find the total horizontal displacement:
which is the position of launch and
which is the range.
3. MAXIMUM HEIGHT
To find the maximum height we replace in the :