Two interacting particles from a closed system whose centre of inertia is at rest. Figure illustrates the positions of both particles at a certain moment and the trajectory of the particle of mass `m_2`. Draw the trajectory of the particle of mass `m_2` if `m_2=m_1//2`.

Explanation

As the closed system consisting two particles `m_1` and of `m_2` is initially at rest the C.M. of the sytem will remain at rest. Further as `m_2=m_1//2`, the C.M. of the sytem divides the line joining `m_1` and `m_2` at the moments of time in the ratio `1:2`. In addition to it the total linear momentum of the system at all the times is zero. So `vecp_1=-vecp_2` and therefore the velocities of `m_1` and `m_2` are also directed in opposite sense. Bearing in mind all these thing, the sought trajectory is as shown in the figure.