Your vessel has a displacement of 19,800...

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Question 1 of 2066636eec28f7522a1c51d0e8

Your vessel has a displacement of 19,800 tons. It is 464 feet long, and has a beam of 64 feet. You have timed its rolling period to be 21.0 seconds in still water. What is your vessel's approximate GM?

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🔍 Key Concepts

• Rolling period (T) and how it relates to metacentric height (GM) • The common approximate GM formula used in stability problems that involves beam (B) and rolling period (T) • Effect of a long rolling period on vessel stability (stiff vs tender ship)

💭 Think About

• First, recall or look up the standard approximate formula that relates GM to the ship’s beam and its observed rolling period in still water. Write that formula down. • Substitute the known values for beam (64 ft) and rolling period (21.0 s) into the formula and be careful with squaring and order of operations. • Before picking an answer, think conceptually: does a long roll period like 21 seconds suggest a large GM (very stiff) or small GM (tender)? Does your numerical result fit that idea?

✅ Before You Answer

• Verify you are using the correct empirical formula for GM that includes a constant (e.g. around 0.44 when using feet and seconds). • Double-check your calculator steps: square only the correct terms and keep track of parentheses. • Compare your computed GM to the answer choices and confirm it is physically reasonable for a large vessel with a 21-second roll period (tender vs stiff).

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