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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?

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.FOM: Focus On Modeling: Vectors Fields
Problem 11P
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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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