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Which table correctly displays the information provided within the problem below? A train travels 8.81 m/s in a -51.0° direction. The train accelerates for 2.23 s, changing its velocity to 9.66 m/s in a 37.0° direction. What is Ax?

Which table correctly displays the information provided within the problem below? A train travels 8.81 m/s in a -51.0° direction. The train accelerates for 2.23 s, changing its velocity to 9.66 m/s in a 37.0° direction. What is Ax?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Kinematic Problem Analysis in Two Dimensions #### Problem Statement: A train travels at a velocity of 8.81 m/s in a direction of -51.0 degrees. It then accelerates for 2.23 seconds, changing its velocity to 9.66 m/s in a direction of 37.0 degrees. Determine the displacement component \(\Delta x\). #### Provided Data: - Initial velocity (\(v_i\)) = 8.81 m/s (at -51.0 degrees) - Final velocity (\(v_f\)) = 9.66 m/s (at 37.0 degrees) - Time interval (\(t\)) = 2.23 s #### Tables for Analysis Three tables (A, B, and C) are provided to determine which correctly displays the given information. ##### Table A: | | x | y | |----|-----|-----| | Vi | 8.81| 0 | | Vf | 0 | 9.66| | a | | -9.80 | | Δx | ? | ? | | t | 2.23| 2.23| ##### Table B: | | x | y | |----|-----|-----| | Vi | 8.81| 8.81| | Vf | 9.66| 9.66| | a | | | | Δx | ? | ? | | t | 2.23| 2.23| ##### Table C: | | x | y | |----|-----|-----| | Vi |5.54 | -6.85| | Vf |7.71 | 5.81 | | a | | | | Δx | ? | ? | | t | 2.23| 2.23| #### Analysis: - **Table A**: Assumes no initial y-component and shows incorrect x and y-components. - **Table B**: Replicates initial and final velocities in both x and y components, which does not reflect directional changes. - **Table C**: Correctly decomposes velocities into x and y components considering angle directions. #### Conclusion: **Table C** correctly displays the given information, using trigonometric components of the velocities to represent changes in x and
Transcribed Image Text:### Kinematic Problem Analysis in Two Dimensions #### Problem Statement: A train travels at a velocity of 8.81 m/s in a direction of -51.0 degrees. It then accelerates for 2.23 seconds, changing its velocity to 9.66 m/s in a direction of 37.0 degrees. Determine the displacement component \(\Delta x\). #### Provided Data: - Initial velocity (\(v_i\)) = 8.81 m/s (at -51.0 degrees) - Final velocity (\(v_f\)) = 9.66 m/s (at 37.0 degrees) - Time interval (\(t\)) = 2.23 s #### Tables for Analysis Three tables (A, B, and C) are provided to determine which correctly displays the given information. ##### Table A: | | x | y | |----|-----|-----| | Vi | 8.81| 0 | | Vf | 0 | 9.66| | a | | -9.80 | | Δx | ? | ? | | t | 2.23| 2.23| ##### Table B: | | x | y | |----|-----|-----| | Vi | 8.81| 8.81| | Vf | 9.66| 9.66| | a | | | | Δx | ? | ? | | t | 2.23| 2.23| ##### Table C: | | x | y | |----|-----|-----| | Vi |5.54 | -6.85| | Vf |7.71 | 5.81 | | a | | | | Δx | ? | ? | | t | 2.23| 2.23| #### Analysis: - **Table A**: Assumes no initial y-component and shows incorrect x and y-components. - **Table B**: Replicates initial and final velocities in both x and y components, which does not reflect directional changes. - **Table C**: Correctly decomposes velocities into x and y components considering angle directions. #### Conclusion: **Table C** correctly displays the given information, using trigonometric components of the velocities to represent changes in x and
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