Explanation Given information: The given expressions are mass = ( 64000 ) ( 2000 ) / 32 slugs. Calculation: This is an application of Newton second law of motion which state that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. F = m a Suppose that the ship is moving in a forward direction then the force due to thrust is acting in such a way that it is pushing the ship forward and resistance of water is a frication force and always acts in the opposite direction of motion, Assume the mass of the ship is m and its acieration is a .Then we can write the equation of motion for the ship as F ︸ T h r u s t − D ︸ D r a g = m a Substitute the values in different quantities, ( a = d v d t ; k = 12 , 000 ) F − k v = m v ' v ' + k m v = F m This is linear first-order ODE which can be solved use the integrating factor method. If a differential equation is in the form. d v d t + p ( t ) v = Q ( t ) Integrating factor is μ ( t ) = exp ( ∫ P ( t ) d t ) and general solution is provided by, μ ( t ) y ( t ) = ∫ ( Q ( t ) ⋅ μ ( t ) ) d t + C Here, μ ( t ) = e ∫ k m d t = e k t m Calculate the general solution by substituting the value of integrating factor μ ( t )

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 14, Problem 48SP

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To find: The general solution of the differential equation.

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Chapter 14, Problem 47SP

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Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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