The car A has a forward speed of 18 km/h and is accelerating at 3.5 m/s². Determine the velocity and acceleration of the car relative to observer B, who rides in a nonrotating chair on the Ferris wheel. The angular rate 2 = 3.8 rev/min of the Ferris wheel is constant.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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## Problem Description:

The car A has a forward speed of 18 km/h and is accelerating at 3.5 m/s². Determine the velocity and acceleration of the car relative to observer B, who rides in a nonrotating chair on the Ferris wheel. The angular rate Ω = 3.8 rev/min of the Ferris wheel is constant.

## Diagram Explanation:

- The diagram shows a Ferris wheel with a radius \( R = 8.7 \, \text{m} \).
- B is an observer riding at an angle of 41° on the Ferris wheel.
- The Ferris wheel rotates with an angular speed \( Ω = 3.8 \, \text{rev/min} \).
- There is an appropriate x-y coordinate system for analysis.
- Car A is moving horizontally towards the right with a given velocity and acceleration.

## Required:

- Determine the relative velocity (\( v_{A/B} \)) of the car A with respect to observer B.
- Determine the relative acceleration (\( a_{A/B} \)) of the car A with respect to observer B.

## Answers:

### Relative Velocity (\( v_{A/B} \)):

\[ v_{A/B} = (\_\_\_\_\_) i + (\_\_\_\_\_) j \, \text{m/s} \]

### Relative Acceleration (\( a_{A/B} \)):

\[ a_{A/B} = (\_\_\_\_\_) i + (\_\_\_\_\_) j \, \text{m/s}^2 \]
Transcribed Image Text:## Problem Description: The car A has a forward speed of 18 km/h and is accelerating at 3.5 m/s². Determine the velocity and acceleration of the car relative to observer B, who rides in a nonrotating chair on the Ferris wheel. The angular rate Ω = 3.8 rev/min of the Ferris wheel is constant. ## Diagram Explanation: - The diagram shows a Ferris wheel with a radius \( R = 8.7 \, \text{m} \). - B is an observer riding at an angle of 41° on the Ferris wheel. - The Ferris wheel rotates with an angular speed \( Ω = 3.8 \, \text{rev/min} \). - There is an appropriate x-y coordinate system for analysis. - Car A is moving horizontally towards the right with a given velocity and acceleration. ## Required: - Determine the relative velocity (\( v_{A/B} \)) of the car A with respect to observer B. - Determine the relative acceleration (\( a_{A/B} \)) of the car A with respect to observer B. ## Answers: ### Relative Velocity (\( v_{A/B} \)): \[ v_{A/B} = (\_\_\_\_\_) i + (\_\_\_\_\_) j \, \text{m/s} \] ### Relative Acceleration (\( a_{A/B} \)): \[ a_{A/B} = (\_\_\_\_\_) i + (\_\_\_\_\_) j \, \text{m/s}^2 \]
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