Problem $3.$

An empty rectangular barge $140$ feet long and $30$ feet wide weighs $504$ tons and has a $KG=6\mathrm{.}5$ feet. It

floats in seawater. The following loading then takes place:

$230$ tons loaded at $4$ ft above keel

$350$ tons loaded at $10$ ft above keel

$120$ tons loaded at $6$ ft above keel

$30$ tons loaded at $13$ ft above keel

The $30$ tons weight listed above is placed $12$ feet off centerline to port. After loading is complete calculate

$(1)$ the displacement, $(2)$ Draft, $(3)$ Transverse metacentric height, $(4)$ Angle of heel