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rain A is traveling at a constant speed VA = 37 mi/hr while car B travels in a straight line along the road as shown at a constant speed VB. conductor C in the train begins to walk to the rear of the train car at a constant speed of 6 ft/sec relative to the train. If the conductor erceives car B to move directly westward at 19 ft/sec, how fast is the car traveling? UB x

rain A is traveling at a constant speed VA = 37 mi/hr while car B travels in a straight line along the road as shown at a constant speed VB. conductor C in the train begins to walk to the rear of the train car at a constant speed of 6 ft/sec relative to the train. If the conductor erceives car B to move directly westward at 19 ft/sec, how fast is the car traveling? UB x

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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### Problem Statement: Train A is traveling at a constant speed \(v_A = 37\) mi/hr while car B travels in a straight line along the road as shown at a constant speed \(v_B\). A conductor C in the train begins to walk to the rear of the train car at a constant speed of 6 ft/sec relative to the train. If the conductor perceives car B to move directly westward at 19 ft/sec, how fast is the car traveling? ### Diagram Explanation: The provided diagram illustrates the scenario where: - Train A is moving on a track from the top-right to the bottom-left of the illustration at a speed \(v_A\). - Car B is moving upwards along a road at a constant speed \(v_B\). - Conductor C is inside the train A and walking towards the rear of the train, which is shown with the vector pointing downward inside the train. - The train's path forms an angle \(\theta\) with the North direction (shown as N), indicating it is heading in a direction that deviates from due North. - The x and y coordinate axes are represented next to the train. ### Calculations: Given Data: - Speed of Train A: \(v_A = 37\) mi/hr - Speed of Conductor C relative to Train A: 6 ft/sec - Perceived speed of Car B by Conductor C: 19 ft/sec westward Steps: 1. Convert relative walking speed of the conductor from ft/sec to mi/hr. \[ 6 \, \text{ft/sec} = (6 \times 3600) \, \text{ft/hr} = 21600 \, \text{ft/hr} \] \[ 1 \, \text{mile} = 5280 \, \text{ft} \] \[ 21600 \, \text{ft/hr} = \frac{21600}{5280} \, \text{mi/hr} = 4.09 \, \text{mi/hr} \] 2. Define the velocity components for Train A and Car B. - Component of Train A’s velocity towards East (horizontal): \(37 \, \cos(\theta)\) - Component of Train A’s velocity towards North (vertical): \(37 \, \sin(\theta)\) - Conductor walks to the rear, reducing
Transcribed Image Text:### Problem Statement: Train A is traveling at a constant speed \(v_A = 37\) mi/hr while car B travels in a straight line along the road as shown at a constant speed \(v_B\). A conductor C in the train begins to walk to the rear of the train car at a constant speed of 6 ft/sec relative to the train. If the conductor perceives car B to move directly westward at 19 ft/sec, how fast is the car traveling? ### Diagram Explanation: The provided diagram illustrates the scenario where: - Train A is moving on a track from the top-right to the bottom-left of the illustration at a speed \(v_A\). - Car B is moving upwards along a road at a constant speed \(v_B\). - Conductor C is inside the train A and walking towards the rear of the train, which is shown with the vector pointing downward inside the train. - The train's path forms an angle \(\theta\) with the North direction (shown as N), indicating it is heading in a direction that deviates from due North. - The x and y coordinate axes are represented next to the train. ### Calculations: Given Data: - Speed of Train A: \(v_A = 37\) mi/hr - Speed of Conductor C relative to Train A: 6 ft/sec - Perceived speed of Car B by Conductor C: 19 ft/sec westward Steps: 1. Convert relative walking speed of the conductor from ft/sec to mi/hr. \[ 6 \, \text{ft/sec} = (6 \times 3600) \, \text{ft/hr} = 21600 \, \text{ft/hr} \] \[ 1 \, \text{mile} = 5280 \, \text{ft} \] \[ 21600 \, \text{ft/hr} = \frac{21600}{5280} \, \text{mi/hr} = 4.09 \, \text{mi/hr} \] 2. Define the velocity components for Train A and Car B. - Component of Train A’s velocity towards East (horizontal): \(37 \, \cos(\theta)\) - Component of Train A’s velocity towards North (vertical): \(37 \, \sin(\theta)\) - Conductor walks to the rear, reducing
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