Launching a Projectile from a Projectile

Suppose a very light secondary projectile is launched from a primary projectile at its apex, with the same speed as the primary (relative to the primary), but at only 2/3 the launch angle. What launch angle maximizes the range of the secondary? 0:00 - Introduction 1:48 - Relative velocity of secondary projectile 5:00 - The kinematics 8:10 - Simplification and non-dimensionalization 13:01 - Results of the quadratic formula (and more simplification) 14:39 - Maximizing 17:46 - Numerical solution and further ideas