Problem $2$: $(14$ points$)$

An identical hockey puck A with velocity of $6\frac{m}{s}$ collides with another identical hockey puck $B$ with velocity of $10\frac{m}{s}.$ The restitution coefficient between hockey pucks A and $B$ is $0\mathrm{.}75.$ Show all work.

a$)$ Draw the appropriate free body and kinetic diagram$($s$).(2$ points$)$

b$)$ Write the momentum conservation equation based on the free body and kinetic diagram$($s$)$ written above. $(2$ points$)$

c$)$ Compute the expression of the restitution coefficient in terms of the velocities. $(2$ points$)$

d$)$ Determine the velocity of hockey puck A just after collision, $(v_A{)}_2.(2$ points$)$

e$)$ Determine the direction of hockey puck A just after collision with respect to the positive $x-$axis. $(1$ points$)$

f$)$ Determine the velocity of hockey puck $B$ just after collision, $(v_B{)}_2.(2$ points$)$

g$)$ Determine the direction of hockey puck $B$ just after collision with respect to the positive $x-$axis. $(1$ points$)$

h$)$ Determine the percentage loss of system kinetic energy, $n.(2$ points$)$