50 N particles P1, P2, P3, ..., PN with masses m, qm, q²m, ..., q-1m, respectively, are at rest at distinct points along a straight line in gravity-free space. The particle P₁ is set in motion towards P2 with velocity V and in every subsequent impact the coefficient of restitution is e, where 0<e < 1. Show that after the first impact the velocities of P1 and P2 are respectively. 1- eq 1+q 1+e V and V₁ + Show that if q<e, then there are exactly N - 1 impacts and that if qe, then the total loss of kinetic energy after all impacts have occurred is equal to 1 me(1 − e−1)V².