# Physics Cup – TalTech 2022 – Problem 2

By Jaan Kalda (TalTech) in collaboration with Máté Vigh

A boy is periodically running around an equilaterally triangular house of side length $a$ on an icy field. What is the minimum duration of one loop around the house, assuming an optimal trajectory? You may assume a constant coefficient of friction $\mu$ between the ice and the boy and that the boy’s stride length is negligible compared to the house’s dimensions. Gravitational acceleration is $g$.

Please submit the solution to this problem via e-mail to physcs.cup@gmail.com. First hints will appear here on 2nd January 2022. After the publication of the first hint, the base score is reduced to 0.9 pts. For full regulations, see the “Participate” tab. The first intermediate results for the Problem 2 will be drawn after 13:00 GMT, 26th December 2021.