Coasting battleship Suppose that an Iowa class battleship has mass around 51,000 metric tons $(51,000,000 \mathrm{kg})$ and a $k$ value in Equation (1) of about 59,000 kg/sec. Assume that the ship loses power when it is moving at a speed of $9 \mathrm{m} / \mathrm{sec}$
a. About how far will the ship coast before it is dead in the water?
b. About how long will it take the ship's speed to drop to $1 \mathrm{m} / \mathrm{sec} ?$

Answer

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Calculus 2 / BC

University Calculus: Early Transcendentals

Chapter 16

First-Order Differential Equations

Section 3

Applications

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Video Transcript

in this video, we're gonna go through the answer. It's question number two from chapter 16.3. So we're asked to find how far coasting battleship we'll travel once is as once his power, once it loses power, traveling at nine of a second. He's the same formulas that we used in question. Once they go to the video question one. If you want to see how we derive the formulas s here is the distance from when the shipping power eso to find out how it's gonna coast, we need to find the limit as t goes to infinity. Well, f on a secret infinity this term is gonna go to zero. So we're just gonna be left with vino. I m okay. And if we so street in the values given in the question for these terms, then we get about seven 1000 800 meters. So by inclement is poppy were asked to find how long it will take the ship's speed to drop. The one reads at the second. So we derived this formula for the time and give them Fred to reach a given speed. V E would drive that in depression. One party so again, so streaming in the values for this question, this is approximately equal to 1900 second.

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