$4.$ A $15\mathrm{.}0$ kg block is attached to a very light horizontal spring of force constant $\backslash (500\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash )$ and is resting on a frictionless horizontal table. Suddenly it is struck by a $3\mathrm{.}00$ kg stone traveling horizontally at $\backslash (8\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ to the right, whereupon the stone rebounds at $\backslash (2\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ horizontally to the left. Find the maximum distance that the block will compress the spring after the collision.