Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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### Relative Motion of Train and Car **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 diagram shows: 1. Train A moving on a track at a speed \( v_A = 37 \) mi/hr. 2. Conductor C is walking to the rear of the train at a speed of 6 ft/sec (relative to the train). 3. Car B is traveling at speed \( v_B \) on a road parallel to the train. 4. Coordinate axes \( x \) (eastward) and \( y \) (northward) along with an angle \( \theta \) showing the path direction of car B relative to the train. **Given Data:** - Speed of Train \( v_A = 37 \) mi/hr - Speed of Conductor = 6 ft/sec (relative to the train) - Perceived Speed of Car by Conductor = 19 ft/sec toward west **Conversion Factor:** - To convert speeds from ft/sec to mi/hr, we use the conversion factor: \(1 \) ft/sec = \( 0.681818 \) mi/hr. **Solution:** To solve the problem, the perceived motion must be converted to common units and analyzed using relative velocity principles. The details of the calculation involve: 1. Convert the conductor's speed to mi/hr: \[ 6 \, \text{ft/sec} \times 0.681818 \, (\text{mi/hr per ft/sec}) = 4.09 \, \text{mi/hr} \] 2. Given that the perceived westward speed of the car is 19 ft/sec (relative to the conductor): \[ 19 \, \text{ft/sec} \times 0.681818 \, (\text{mi/hr per ft/sec}) = 12.95 \, \text{mi/hr} \] 3. The relative speed of the car, when perceived by the conductor moving at 4.09 mi/hr, points
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Transcribed Image Text:### Relative Motion of Train and Car **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 diagram shows: 1. Train A moving on a track at a speed \( v_A = 37 \) mi/hr. 2. Conductor C is walking to the rear of the train at a speed of 6 ft/sec (relative to the train). 3. Car B is traveling at speed \( v_B \) on a road parallel to the train. 4. Coordinate axes \( x \) (eastward) and \( y \) (northward) along with an angle \( \theta \) showing the path direction of car B relative to the train. **Given Data:** - Speed of Train \( v_A = 37 \) mi/hr - Speed of Conductor = 6 ft/sec (relative to the train) - Perceived Speed of Car by Conductor = 19 ft/sec toward west **Conversion Factor:** - To convert speeds from ft/sec to mi/hr, we use the conversion factor: \(1 \) ft/sec = \( 0.681818 \) mi/hr. **Solution:** To solve the problem, the perceived motion must be converted to common units and analyzed using relative velocity principles. The details of the calculation involve: 1. Convert the conductor's speed to mi/hr: \[ 6 \, \text{ft/sec} \times 0.681818 \, (\text{mi/hr per ft/sec}) = 4.09 \, \text{mi/hr} \] 2. Given that the perceived westward speed of the car is 19 ft/sec (relative to the conductor): \[ 19 \, \text{ft/sec} \times 0.681818 \, (\text{mi/hr per ft/sec}) = 12.95 \, \text{mi/hr} \] 3. The relative speed of the car, when perceived by the conductor moving at 4.09 mi/hr, points
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