### Homework Problem: Relative Velocity and Acceleration in Rotating Frames**Problem Statement:**The car \(A\) has a forward speed of 21 km/h and is accelerating at \( 3.0 \, \text{m/s}^2 \). 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 \( \Omega = 3.2 \, \text{rev/min} \) of the Ferris wheel is constant.**Given Data:**- Forward speed of car \( A \): \( 21 \, \text{km/h} \)- Acceleration of car \( A \): \( 3.0 \, \text{m/s}^2 \)- Radius of the Ferris wheel: \( R = 8.4 \, \text{m} \)- Angular rate of the Ferris wheel: \( \Omega = 3.2 \, \text{rev/min} \)**Diagram:**The provided diagram depicts:- A Ferris wheel with a radius \( R = 8.4 \) m.- The Ferris wheel has a marked angular rate \( \Omega = 3.2 \, \text{rev/min} \).- Observer \( B \) is seated on a nonrotating chair on the Ferris wheel.- The car \( A \) is moving forward with the given speed and acceleration.**Answers:**To find:1. The velocity of car \( A \) relative to observer \( B \):\[ \vec{v}_{A/B} = ( \quad i \quad \text{m/s} ) \, \vec{i} + ( \quad j \quad \text{m/s} ) \, \vec{j} \]2. The acceleration of car \( A \) relative to observer \( B \):\[ \vec{a}_{A/B} = ( \quad i \quad \text{m/s}^2 ) \, \vec{i} + ( \quad j \quad \text{m/s}^2 ) \, \vec{j} \]Note: Please fill in the blanks \( \quad i \quad \) and \( \quad j \quad \) with the appropriate numerical values derived from calculations, based on the given data and needed conversions

Answered: Image /qna-images/answer/c23ef0d0-bcf1-442e-aa70-22f9b24cd322.jpg

The car A has a forward speed of 21 km/h and is accelerating at 3.0 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 02-3.2 rev/min of the Ferris wheel is constant. 02=3.2 rev/min B R 8.4 ml j) m/s j) m/s² Answers: VA/B aA/B i i i+ i i+ i

The car A has a forward speed of 21 km/h and is accelerating at 3.0 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 02-3.2 rev/min of the Ferris wheel is constant. 02=3.2 rev/min B R 8.4 ml j) m/s j) m/s² Answers: VA/B aA/B i i i+ i i+ i

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Conservation of Energy

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Question

### Homework Problem: Relative Velocity and Acceleration in Rotating Frames

**Problem Statement:**

The car \(A\) has a forward speed of 21 km/h and is accelerating at \( 3.0 \, \text{m/s}^2 \). 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 \( \Omega = 3.2 \, \text{rev/min} \) of the Ferris wheel is constant.

**Given Data:**
- Forward speed of car \( A \): \( 21 \, \text{km/h} \)
- Acceleration of car \( A \): \( 3.0 \, \text{m/s}^2 \)
- Radius of the Ferris wheel: \( R = 8.4 \, \text{m} \)
- Angular rate of the Ferris wheel: \( \Omega = 3.2 \, \text{rev/min} \)

**Diagram:**

The provided diagram depicts:
- A Ferris wheel with a radius \( R = 8.4 \) m.
- The Ferris wheel has a marked angular rate \( \Omega = 3.2 \, \text{rev/min} \).
- Observer \( B \) is seated on a nonrotating chair on the Ferris wheel.
- The car \( A \) is moving forward with the given speed and acceleration.

**Answers:**

To find:
1. The velocity of car \( A \) relative to observer \( B \):
\[ \vec{v}_{A/B} = ( \quad i \quad \text{m/s} ) \, \vec{i} + ( \quad j \quad \text{m/s} ) \, \vec{j} \]

2. The acceleration of car \( A \) relative to observer \( B \):
\[ \vec{a}_{A/B} = ( \quad i \quad \text{m/s}^2 ) \, \vec{i} + ( \quad j \quad \text{m/s}^2 ) \, \vec{j} \]

Note: Please fill in the blanks \( \quad i \quad \) and \( \quad j \quad \) with the appropriate numerical values derived from calculations, based on the given data and needed conversions

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