Problem $4(20$ pts$)$: In the position shown in Figure $4$ block $\backslash ($ B $\backslash )$ just contacts the spring. Block $\backslash ($ A $\backslash )$ impacts block $\backslash ($ B $\backslash )$ with a velocity of $\backslash (8\backslash$mathrm$\{$ft$\}/\backslash$mathrm$\{$s$\}\backslash ).$ The weight of block $\backslash ($ A $\backslash )$ is $2$ lb $,$ and the weight of block $\backslash ($ B $\backslash )$ is $3$ lb $.$

$($a$)$ Find the velocities of each block after impact.

$($b$)$ Find the maximum distance through which the spring is compressed, if the impact is elastic and the plane surface is frictionless.

Figure $4$

Bonus $2(10$ pts$)$: Answer questions $($a$)$ and $($b$)$ in Problem $5$ if the coefficient of restitution is $0\mathrm{.}5,$ and the coefficient of friction between the blocks and surface is $0\mathrm{.}25.$