A $15\mathrm{.}0kg$ block is attached to a very light horizontal

spring of force constant $575\frac{N}{m}$ and is resting on

a smooth horizontal table $($Figure $1).$ Suddenly it is

struck by a $3\mathrm{.}00kg$ stone traveling horizontally at

$8\mathrm{.}00\frac{m}{s}$ to the right, whereupon the stone

rebounds at $2\mathrm{.}00\frac{m}{s}$ horizontally to the left.

Part A

Find the maximum distance that the block will compress the spring after the collision. $($Hint: Break this problem into two parts $-$

the collision and the behavior after the collision $-$ and apply the appropriate conservation law to each part.$)$

Express your answer in meters.

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