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Q2. The ‘wall sided formula’ gives an expression for righting lever (GZ) as follows:  GZ = sin θ (GM + ½ BM tan2 θ) (a) Derive an expression for the `angle of loll' of a ship which is initially unstable in still water, using the wall sided formula. (b) A box shaped vessel designed to carry timber, is 80 m long, 12 m wide and floats at a draught of 5 m in sea water of density 1025 kg/m3 with a KG of 4.815 m. A beam wind acts on the exposed area of the vessel causing it to heel to an angle of 15°. The heeling moment caused by the wind is given by the expression: Heeling moment = 0.85 A b v2 cos2 θ Nm

where:  A = exposed area = 627 m2 b = lever = 6.5 m      v = wind speed in m/s                                        θ = angle of heel in degrees.

Calculate the wind speed in knots, using the wall sided formula for GZ.