A thin light string is wrapped around the outer rim of a uniform hollow cylinder of mass $4\mathrm{.}55kg$ having inner and

outer radii as shown in the figure $($Figure $1).$ The cylinder is then released from rest.

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Part A$)$

How far must the cylinder fall before its center is moving at $6\mathrm{.}48$ m$/$s

$?$

Express your answer in meters.

Part B$)$

If you just dropped this cylinder without any string, how fast would its center be moving when it had fallen the distance in part A$?$

Express your answer in meters per second.