$.$ A $0\mathrm{.}50$ kg puck moving at $4\mathrm{.}0$ m$/$s $[$E$]$ is sliding on a frictionless horizontal air table. It undergoes an elastic head$-$on collision with another puck of mass $0\mathrm{.}90$ kg$,$ moving at $3\mathrm{.}0$ m$/$s $[$W$].$ The pucks are in contact for $0\mathrm{.}20$ s$.(8$ marks$)$ a$)$ Find the velocity of each puck after the collision. b$)$ Calculate the change in momentum of the $0\mathrm{.}50$ kg puck. c$)$ Calculate the average force exerted on the smaller puck by the larger one.