Make use of the fact that if the boy runs always on the verge of slipping, the length of the curve drawn in the v_x-v_y plane is proportional to the running time: a fixed running time corresponds to a fixed curve 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, 16th January 2022, together with the next updates of the intermediate results.