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Train 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 ve- 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? UB C mi/hr B Answer: ve i NIO

Train 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 ve- 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? UB C mi/hr B Answer: ve i NIO

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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**Relative Motion Analysis Problem:** **Problem Statement:** Train A is traveling at a constant speed \(v_A = 37 \, \text{mi/hr}\) 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 Description:** - The diagram shows Train A traveling on a railway track inclined at an angle \(\theta\) to the x-axis. - Car B is traveling on a parallel road to the left of the railway track. - There are axes labeled x and y, with y being perpendicular to the railway track and x being parallel to it. - The speed of car B, \(v_{B}\), is marked as a vector pointing towards the north-west direction. - Several labels such as \(v_A\), \(v_B\), and \(\theta\) are placed next to their respective paths and directions. **Mathematical Formulation:** Given: - \(v_A = 37 \, \text{mi/hr}\) - Conductor C walking at \(6 \, \text{ft/sec}\) towards the rear of the train. - Car B appears to be moving at \(19 \, \text{ft/sec}\) directly westward to the conductor. Required: - Determine the speed \(v_B\) of car B. **Conversion Factors:** - 1 mile = 5280 feet - 1 hour = 3600 seconds - Therefore, \(1 \, \text{mi/hr} = \frac{5280}{3600} \approx 1.467 \, \text{ft/sec}\) Convert the speed of Train A from mi/hr to ft/sec: \[ v_A = 37 \, \text{mi/hr} \times 1.467 = 54.279 \, \text{ft/sec} \] The relative speed of the car B perceived by the conductor, \( v_{BC} \), is given as 19 ft/sec westward. Using relative motion principles: \[ \vec{v}_{B/C} = \vec{v}_B - \vec{v}_A - \
Transcribed Image Text:**Relative Motion Analysis Problem:** **Problem Statement:** Train A is traveling at a constant speed \(v_A = 37 \, \text{mi/hr}\) 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 Description:** - The diagram shows Train A traveling on a railway track inclined at an angle \(\theta\) to the x-axis. - Car B is traveling on a parallel road to the left of the railway track. - There are axes labeled x and y, with y being perpendicular to the railway track and x being parallel to it. - The speed of car B, \(v_{B}\), is marked as a vector pointing towards the north-west direction. - Several labels such as \(v_A\), \(v_B\), and \(\theta\) are placed next to their respective paths and directions. **Mathematical Formulation:** Given: - \(v_A = 37 \, \text{mi/hr}\) - Conductor C walking at \(6 \, \text{ft/sec}\) towards the rear of the train. - Car B appears to be moving at \(19 \, \text{ft/sec}\) directly westward to the conductor. Required: - Determine the speed \(v_B\) of car B. **Conversion Factors:** - 1 mile = 5280 feet - 1 hour = 3600 seconds - Therefore, \(1 \, \text{mi/hr} = \frac{5280}{3600} \approx 1.467 \, \text{ft/sec}\) Convert the speed of Train A from mi/hr to ft/sec: \[ v_A = 37 \, \text{mi/hr} \times 1.467 = 54.279 \, \text{ft/sec} \] The relative speed of the car B perceived by the conductor, \( v_{BC} \), is given as 19 ft/sec westward. Using relative motion principles: \[ \vec{v}_{B/C} = \vec{v}_B - \vec{v}_A - \
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