Program Explanation Given information: The value of a is 100 mi , the speed of plane relative to wind is v 0 = 400 mi / h and the speed of wind is w = 40 mi / h . The solution of differential equation that satisfies the equation of plane trajectory is, y ( x ) = a 2 [ ( x a ) 1 − k − ( x a ) 1 + k ] ....... (1) Explanation: The value of constant k is, k = w v o = 40 400 = 1 10 Substitute 100 for a and 1 10 for k in equation (1). y ( x ) = 100 2 [ ( x 100 ) 1 − 1 10 − ( x 100 ) 1 + 1 10 ] = 50 [ ( x 100 ) 9 10 − ( x 100 ) 11 10 ] = 50 [ x 9 10 100 9 10 − x 11 10 100 11 10 ] Differentiate the above equation with respect to x . d y d x = 50 [ 9 10 ⋅ 100 9 10 x 9 10 − 1 − 11 10 ⋅ 100 11 10 x 11 10 − 1 ] = 50 [ 9 10 ⋅ 1 100 ⋅ 100 − 1 10 ⋅ x − 1 10 − 11 10 ⋅ 1 100 ⋅ 100 1 10 ⋅ x<

5th Edition

ISBN: 9780321974235

Author: Calvis

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

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Question

Chapter 1.6, Problem 69P

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Program Description: Purpose ofproblem is to calculate the distance that the wind blows the airplane.

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Chapter 1.6, Problem 68P

Chapter 1.6, Problem 70P

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Chapter 1 Solutions

EBK DIFFERENTIAL EQUATIONS

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Program Description: Purpose ofproblem is to calculate the distance that the wind blows the airplane.

Solution Summary: The author explains the purpose of the problem, which is to calculate the distance that the wind blows the airplane.

Program Description: Purpose ofproblem is to calculate the distance that the wind blows the airplane.

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Chapter 1 Solutions