To calculate the height Shaun White needs to complete a 3.5-second trick, the discussion emphasizes using kinematic equations and the conservation of energy principles. The initial velocity when leaving the halfpipe is crucial, as it will not be zero, and it relates to the velocity upon re-entry. The participants explore the relationship between exit and entry velocities, concluding that they are equal in magnitude but opposite in direction. The calculations suggest that the maximum height can be derived from these velocities and the known acceleration due to gravity. Ultimately, the discussion focuses on solving for the correct initial velocity and height using the appropriate kinematic equations.