The optimal release angle for a projectile launched from a pendulum is the unique root of a cubic equation in cos of the angle, and it increases monotonically from 0 to 45 degrees as initial speed grows.
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Theoretical analysis of the maximum range of a projectile released from a pendulum
The optimal release angle for a projectile launched from a pendulum is the unique root of a cubic equation in cos of the angle, and it increases monotonically from 0 to 45 degrees as initial speed grows.