In order to check your vessel's stability, a weight of 40 tons is lifted with the jumbo boom, the boom head being 50 feet from the ship's centerline. The clinometer is then carefully read and shows a list of 5°. The vessel's displacement is 8,000 tons including the suspended weight. What will be the metacentric height of the vessel at this time?

Question

In order to check your vessel's stability, a weight of 40 tons is lifted with the jumbo boom, the boom head being 50 feet from the ship's centerline. The clinometer is then carefully read and shows a list of 5&deg;. The vessel's displacement is 8,000 tons including the suspended weight. What will be the metacentric height of the vessel at this time?

Accepted Answer

Option C: 2.86 feet. Utilize the formula GM = (w * d) / (Displacement * tan(theta)) to determine the metacentric height. Substituting the given parameters: (40 tons * 50 feet) / (8000 tons * tan(5 degrees)) = 2000 / (8000 * 0.08749) = 2000 / 699.9 = 2.857 feet. Rounding to the nearest hundredth provides the correct value of 2.86 feet.