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Q2. The ‘ wall sided formula ‘ gives an expression for  righting lever ( GZ) as follows:

GZ=sinθ (GM+ 1/2  BM tan² θ)

(a) Using the wall sided formula, derive an expression for the angle of loll of a ship which is initially unstable in still water.(5)

(b) A box shaped vessel is 40 m long, 10 m wide and floats at a draught of 4 m in sea water of density 1025 kg/m³ with a KG of 3.883 m.

A beam wind acts on the exposed area of the vessel causing it to heel to an angle of 12^o.

The heeling moment caused by the wind is given by the expression:

Heeling moment = 850 v²  cos² θ Nm

where: v = wind speed in m/s

θ= angle of heel in degrees

Calculate the wind speed using the wall sided formula for GZ.  (11)