Program Explanation Given information: The nuclear wastes in drums with weight W and volume V drop into the ocean. W = 640 lb V = 8 ft 3 v 0 = 0 y 0 = 0 The force equation for a drum falling through water is calculated as, m d v d t = − W + B + F R Here, the buoyant force B is equal to the weight at 62.5 lb / ft 3 of the volume of water displaced by the drum. B = ( 62.5 ⋅ 8 ) lb =500 lb The force of water resistance is F R . The empirical value of F R is 1 pound for each foot per second of the velocity of a drum. F R = − 1 v ( t ) = − v ( t ) The drums are likely to burst upon the impact of more than 75 ft / s . Explanation: Substitute all defined constants in the differential equation m d v d t = − W + B + F R as shown below. 20 d v d t = − 640 + 500 − v Solve the differential equation as follows: 20 d v d t = − 140 − v d v d t = − 7 − 1 20 v d v 7 + 1 20 v = − d t ∫ 0 v d v 7 + 1 20 v = − ∫ 0 t d t Further solve the above equation as follows: 20 ln ( 7 + 1 20 v ) − 20 ln 7 = − t ln ( 1 + 1 140 v ) = − t 20 1 + 1 140 v = e − t 20 v (

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ISBN: 9780135962176

Author: Edwards

Publisher: PEARSON CO

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A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exp…

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Chapter 2.3, Problem 12P

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Program Description: Purpose of the problem is to obtain the maximum depth to which nuclear waste drums can be dropped in the ocean without likelihood of bursting.

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Chapter 2.3, Problem 11P

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Program Description: Purpose of the problem is to obtain the maximum depth to which nuclear waste drums can be dropped in the ocean without likelihood of bursting.

Solution Summary: The author explains that the problem is to obtain the maximum depth to which nuclear waste drums can be dropped in the ocean without likelihood of bursting.

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Program Description: Purpose of the problem is to obtain the maximum depth to which nuclear waste drums can be dropped in the ocean without likelihood of bursting.

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Chapter 2 Solutions