Force of friction is not always isotropic. Often the magnitude and direction of a friction force depend on the direction of body motion. For example, friction anisotropy can arise in the presence of "grooves" of a certain orientation on the contact surface of bodies (it is known that the coefficient of friction of oak against oak along and across the grain is equal to 0.48 and 0.34, respectively). Friction anisotropy can lead to unusual properties of motion which are studied in this problem.
Suppose that a surface is made of an anisotropic material. One of the most popular models of anisotropic friction suggests that there are perpendicular axes $X$ and $Y$ (they are called \textit{primary}) so that the friction force $\vec F$ acting on a body will depend on the direction of the body motion as
\begin{matrix} F_x &=-\dfrac{|N|}{|v|} \mu_x v_x \\ F_y &=-\dfrac{|N|}{|v|} \mu_y v_y \end{matrix}
where $F_x$ and $F_y$ are the friction force components, $N$ is a normal reaction force acting on the body, $v_x$ and $v_y$ are components of the velocity vector $\vec v$, and $\mu_x$ and $\mu_y$ are the friction coefficients along the primary axes.
Hereinafter, it is understood that the coordinate axes on the plane coincide with the primary axes. The friction coefficients are $\mu_x = 0,\!75$ and $\mu_y = 0,\!5$ unless otherwise stated.
In parts A and B a body can be considered as point-like. The plane, on which the bodies move, is horizontal in all parts of the problem.
Provide a numerical answer wherever possible.
Two identical point-like masses $m$ are connected with a weightless inextensible rod of length $L=1~\text{m}$, the system lies on a surface with anisotropic friction. The rod is aligned with the $Y$ axis and does not touch the surface. One of the masses is given an initial velocity perpendicular to the rod.