8.9 As depicted in figure 5, a point mass \(m\) is placed in the centre of a box of mass \(m\) . Initially, the mass is given initial velocity \(v_0\) . Assuming that after every collision, the relative velocity of the colliding bodies is decreased by a factor \(\epsilon\), determine a) the velocity-time graph of the box. b) After some time has passed, to what value will the velocity of the box tend towards? c) given \(\epsilon = \sqrt[4]{0.5}\) , what is the maximum number of collisions before the system loses more than 40% of its initial energy?