Optimal trajectory of an observer tracking the motion of an object equipped with a striking device

An object $t$ equipped with a high-speed striking device moves along a given trajectory $\mathscr{T}$. The object is tracked by a spatial observer $f$, which has to hide behind convex fragments of the environment. A method is proposed for constructing an observer trajectory $\mathscr{T}_f$ that makes it possible to track the motion of the object on as long a segment of $\mathscr{T}$ as possible. Under the assumption that the observer leaves for a shelter along $\mathscr{T}_f$ at a constant maximum speed, the object $t$ chooses an optimal mode of speed on its trajectory.