Question 40
Let $P_0,P_1,\ldots,P_{2021}$ be points on the unit circle with center $O$, such that for every $n\in\{1,2,\ldots,2021\}$, the length of the counterclockwise arc from $P_{n-1}$ to $P_n$ belongs to $[\pi/2,\pi]$.
Find the maximum length of the vector
$$
\overrightarrow{OP_0}+\overrightarrow{OP_1}+\cdots+\overrightarrow{OP_{2021}}.
$$
Find the maximum length of the vector
$$
\overrightarrow{OP_0}+\overrightarrow{OP_1}+\cdots+\overrightarrow{OP_{2021}}.
$$