The DEEP DRILLER, at a draft of 60 feet and a total vertical moment of 1,012,598 foot-tons, pumps 2,068.7 long tons of ballast overboard. The VCG of the discharged ballast is 15.0 feet. What is the new height of the center of gravity?
• Vertical center of gravity (VCG) is found by dividing the total vertical moment by the total displacement (in long tons). • When you remove weight, you must subtract both the weight and its moment from the ship’s totals before recomputing VCG. • A weight removed below the current VCG will tend to raise the new VCG; a weight removed above the current VCG will tend to lower it.
• First, find the vessel’s original displacement using the given total vertical moment and original VCG at 60 feet. • Next, calculate the moment of the ballast being discharged and subtract it from the original total moment; do the same with the displacement. • Once you have the new total moment and new displacement, divide to obtain the new VCG, then compare it with the choices. • Before doing any math, think: the ballast VCG is 15 feet and the ship’s VCG is around 60 feet—should the final VCG be higher or lower than 60? Use that to eliminate wrong answers.
• Confirm that you are using consistent units: long tons for weight and foot-tons for moments. • Be sure you subtract the discharged weight and its moment (do not add). • After calculating, check whether your new VCG trend (up or down) matches the physical expectation of removing a low weight from a higher VCG vessel.
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