A bullet with mass m $=10\mathrm{.}0$ g bullet is fired into a block with mass M $=2\mathrm{.}20$ kg which is

attached to a spring with a force constant of $23\mathrm{.}3$ N$/$m$.$ The bullet has a speed of $300$ m$/$s just before it

strikes the block and the block slides on a frictionless surface. $($THIS IS AN EXAM QUESTION.$)$

$8.)$ Find how far the spring is compressed in units of cm$.$

$($A$)9\mathrm{.}02($B$)41\mathrm{.}8($C$)55\mathrm{.}3($D$)49\mathrm{.}7($E$)14\mathrm{.}3$

$9.)$ After the spring is compressed, the system undergoes simple harmonic motion. Find the magnitude

of the velocity when the block $($with embedded bullet$)$ is a half$-$way through a full amplitude. Give

an answer in m$/$s$.$

$($A$)1\mathrm{.}18($B$)5\mathrm{.}41($C$)3\mathrm{.}24($D$)1\mathrm{.}67($E$)8\mathrm{.}12$