Question $1.$

A rectangular pontoon $12m$ wide, $20m$ long and $5m$ deep is floating in water. It assumes the position shown when a load of $PN$ is added to the deck in the position shown. G is the centre of gravity of the pontoon alone and B is the centre of buoyancy of the floating pontoon with the load $P$ in place. and dotted line bisects XP$)$

$($a$)$ Show that $SK=0\mathrm{.}642m$ and find GS$.$

$($b$)$ What is the weight of the pontoon?

$($c$)$ What is the load P$?$

$($d$)$ What is the metacentric height of the combined pontoon and the load $P$ when $P$ is moved to the centerline of the pontoon such that the CG of the load is $1m$ above the deck?

$($e$)$ What is the angle of tilt when $P$ is move to a location $1m$ from the centerline of the pontoon?