For a projectile launched with a velocity v at an angle to the horizonal of
where t is the time in motion. On a level plane where the projectile lands at the same altitude as it was launched, a derivative of the maximum height shows that it is reached after a time
where g is the gravitational acceleration. The range is then the distance traveled in time ( up and down),
Ballistics, Distance, Height, Trajectory
References
O'Hanian, H. C. "The Motion of Projectiles." §4.3 in Physics, Vol. 1. New York: W. W. Norton, pp. 71-76, 1985.