Build a mapping between two problems: (a) finding the maximal average velocity in the direction of the x-axis for a curve of fixed length and fixed endpoints in v_x-v_y plane; finding the maximal x-coordinate of the center of mass for a rope of fixed endpoints and fixed length.
Please submit the solution to this problem via e-mail to physcs.cup@gmail.com. The next hint for the Problem 2 will be published at 13:00 GMT, 23rd January 2022, together with the next updates of the intermediate results.