Explanation Given: The model of velocity is m d v d t = − m g − k v . Procedure used: 1. Write the circuit equation. 2. Find the integrating factor. 3. Obtain the final solution of differential equation. 4. Substitute the condition to obtain the constant value. Calculation: The model of velocity is given by, m d v d t = − m g − k v (1) The solution of differential equation is, v ( I .F ) = ∫ − g ( I .F ) d t + c (2) Obtain integrating factor of differential equation in equation (1). I .F = e ∫ k m d t I .F = e k m t Substitute e k m t for I .F in equation (2) and integrate. v ( e k m t ) = ∫ − g ( e k m t ) d t + c v ( e k m t ) = − g m k ( e k m t ) + c (3) Substitute 0 for t and 300 for v in equation (3). 300 = − g m k ( e k m t ) + c c = g m k + 300 Substitute g m k + 300 for c in equation (3) v ( e k m t ) = − g m k ( e k m t ) + g m k + 300 v ( t ) = − g m k + ( 300 + g m k ) e − k m t (4) Integrate equation (4) for s ( t ) and substitute 0 for t and 0 for s

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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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 2.7, Problem 37E

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Chapter 2.7, Problem 36E

Chapter 2.7, Problem 38E

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The maximum height attained by the cannonball must be less than that in part (b) of Problem 36 .

Solution Summary: The author explains that the maximum height attained by the cannonball must be less than that in part (b) of Problem 36.

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Chapter 2 Solutions