To achieve maximum hang time on a 65-yard kick, the kicker must determine the optimal angle for the kick, which involves solving equations related to projectile motion. The key variables include the initial velocity of 27 yards/sec and the gravitational acceleration, which can be converted to yards. The discussion emphasizes the need to separate horizontal and vertical motion equations to solve for the angle, θ, while eliminating the time variable. Participants explore the relationships between the angle, distance, and time of flight, ultimately concluding that there are two potential angles that could yield the desired hang time. Understanding these calculations is crucial for maximizing the effectiveness of the kick.