Problem 11340 of The American Mathematical Monthly

Problem 11340 of The American Mathematical Monthly (January 2008) asks for the following:

Given a disk centered at the origin that rotates counterclockwise with a uniform angular velocity in the - plane, point masses fly off the disk's rim along its tangents. Once they have left the disk, they freely fall downward under the influence of gravity. All point masses that leave the disk rim from its right half have an upward initial velocity component and reach a maximum height before falling. (All point masses that leave the disk rim from the left half have their maximum height at their starting point.) Find an implicit description of the envelope curve of the points of maximum height for the point masses leaving the disk on the right half.

This Demonstration shows the trajectories of the point masses, the points of maximum height of the point masses that leave the rim on the right half, and the envelope.