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A vector field representing wind speeds is given by v = æy³ i + 3x³y³j. %3D A walker can take one of two paths between points A(0,0) and B(1,1). Determine which path has more work done by the field?

A vector field representing wind speeds is given by v = æy³ i + 3x³y³j. %3D A walker can take one of two paths between points A(0,0) and B(1,1). Determine which path has more work done by the field?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A vector field representing wind speeds is given by v = ry³ i + 3x³y³j. A walker can take one of two paths between points A(0,0) and B(1,1). Determine which path has more work done by the field? a) The first path follows y = x4. Find the work done by the field following this path. For path c1, v • dr =( )dr Sa v• dr = Note: Show solution to integral as answer rounded to 2 decimal places. b) The second path follows y = x. Find the work done by the field following this path. For path c2, v • dr =( )dx S,v• dr Note: Show solution to integral as answer rounded to 2 decimal places. c) Which path should you take if you want to put in less effort? O Path on curve 1 O Path on curve 2 O Either path, effort is the same.
Transcribed Image Text:A vector field representing wind speeds is given by v = ry³ i + 3x³y³j. A walker can take one of two paths between points A(0,0) and B(1,1). Determine which path has more work done by the field? a) The first path follows y = x4. Find the work done by the field following this path. For path c1, v • dr =( )dr Sa v• dr = Note: Show solution to integral as answer rounded to 2 decimal places. b) The second path follows y = x. Find the work done by the field following this path. For path c2, v • dr =( )dx S,v• dr Note: Show solution to integral as answer rounded to 2 decimal places. c) Which path should you take if you want to put in less effort? O Path on curve 1 O Path on curve 2 O Either path, effort is the same.
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