A small, $m=0\mathrm{.}5kg$ block is released from rest on a smooth, frictionless track $h=3\mathrm{.}5m$ above the floor $($see Fig. $1$ below$).$ When this block reaches the bottom of the track, it makes a smooth transition into sliding on a level track which is also frictionless, except between point A and point $B($separated by $d=1\mathrm{.}5m)$ where the coefficient of kinetic friction is ${}_k=0\mathrm{.}4.$ A little beyond point $B$ the block hits a spring with $k=80\frac{N}{m}.$

$($a$)$ Compute the distance $x$ the spring is compressed upon collision with the block.

$($b$)$ Compute the height to which the block rebounds.

$($c$)$ Where does the block come to rest with respect to point $A?$