The first real hint will be published on 11th April. Meanwhile, here are the clarifications regarding the grading of Problem 4.
The solutions with good physics received thus far can be divided into two classes: (a) the solutions which are valid if u\ll \sqrt{k_BT/m}\sqrt{k_BT/U_0}, and (b) the solutions which are valid if u\gg \sqrt{k_BT/m}\sqrt{k_BT/U_0}. There is a very little room for the case (b) since according to the conditions of the problem, u\ll \sqrt{k_BT/m}. However, \sqrt{k_BT/U_0}=0.1 and so the case (b) is still somewhat possible. So, I decided to split the grading of the problem into two parts: explaining correctly the physics of the case (b) (while not necessarily writing down the final answer, because there is almost no room in the parameter space for this case) will be \frac 12 of the full point, and obtaining the correct answer for the case (a) will give an additional \frac 12 of the full point. The speed bonuses for the case (a) and the case (b) are counted separately, but the best solution award will be given for the problem as a whole. A completely wrong solution will incur a penalty for the both sub-scores, but a correct solution for the case (b) without considering correctly the case (a) will not bring any penalty for the sub-score of (a), and the other way around.
Those solutions which exhibit a partial qualitative understanding of the processes will be graded as “almost correct”, i.e. will receive a partial penalty for the both parts.
Please submit the solution of this problem via e-mail to physcs.cup@gmail.com.
For full regulations, see the “Participate” tab.