Marinada '22

[lang=hr] Sada su Alice i Bob napravili mali pokus s loptom. Pomicali su strelice po krivuljama tako da kut između strelice i krivulje bude konstantan. (slika 1) \begin{figure} \centering \includegraphics[scale=0.5]{p21.jpeg} \caption{Sketch 1} \end{figure} Dvojac je micao strelice prateći prvo zelenu pa narančastu petlju (slika 2). Koliko iznosi kut (u radijanima) između početne i konačne strelice na kraju petlje? \begin{figure} \centering \includegraphics[scale=0.5]{p22.jpeg} \caption{Sketch 2} \end{figure} Za ovaj zadatak pretpostavite da je $\alpha=1, a=1, b=1$ (svi kutovi su u radijanima). Odgovor napišite kao dva broja (zelena, narančasta) odvojena zarezom i zaokružena na 2 decimale. [/lang] [lang=en] Bob and Alice now do a little expirment with the ball. Moving an arrow along curves in such a manner that the angle between curve and arrow stays the same (as in sketch 1), \begin{figure} \centering \includegraphics[scale=0.5]{p21.jpeg} \caption{Sketch 1} \end{figure} The two move an arrow along the green and orange loop in sketch 2 respectively. What is the angle (in radian) between the the initial arrow and the arrow at the end of the loop? \begin{figure} \centering \includegraphics[scale=0.5]{p22.jpeg} \caption{Sketch 2} \end{figure} For this problem, suppose: $\alpha=1, a=1, b=1$ (all angles in radian). You should write your answer as a list of two numbers: angle(green), angle(orange). Round all numbers to two places after decimal \textbf{point}. [/lang]