For a projectile launched with a velocity v at an angle to the horizonal of , the horizontal distance traveled is called the range, and is given by

(1)

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

(2)

where g is the gravitational acceleration. The range is then the distance traveled in time ( up and down),

			(3)
			(4)

Ballistics, Distance, Height, Trajectory