is the moment of inertia for the catapult arm and projectile.
This accleration, when taken over the range of motion of the catapult
arm when firing, will result in an angular velocity w that can
be found with the equation w2=2aq,
range of motion of the catapult arm. Once the projectile is
released, the velocity of the projectile is tangent to the circular
path it was traveling at the point it was released, and is equal to the
angular velocity times the length of the catapult arm, or
is the length of the catapult arm. Once released, the projectile
obeys the laws of projectile motion, which, desregarding air
resistance, give the range as
is the acceleration due to gravity and q is the
angle from horizontal at which the projectile is released.