PROBLEM $13\mathrm{.}26$

A $3-$kg block rests on top of a $2-$kg block supported by$,$ but not attached to$,$ a spring of constant $\backslash (40\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash ).$ The upper block is suddenly removed. Determine $($a$)$ the maximum speed reached by the $\backslash (2-\backslash$mathrm$\{$kg$\}\backslash )$ block, $\backslash (($b$)\backslash )$ the maximum height reached by the $\backslash (2-\backslash$mathrm$\{$kg$\}\backslash )$ block.

Hints:

$($a$)$

Let Position $1$: Block B has just been removed.

Let position $2$ be a later position while the spring still contacts block $\backslash ($ A $\backslash ).$

$($b$)$

Let Position $3$: Block A reaches maximum height. Assume that the block has separated from the spring. Spring force is zero at separation.