### Ferris Wheel Car Problem**Problem Statement:**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 non-rotating chair on the Ferris wheel. The angular rate Ω = 3.2 rev/min of the Ferris wheel is constant.**Diagram:**![Diagram](image-link)- The Ferris wheel has a radius \( R = 8.4 \) m.- The angle at which the observer B is located from the horizontal axis is 44°.- The Ferris wheel has an angular rate \( \Omega = 3.2 \) rev/min.- The car A is moving along a straight path on the ground.**Given:**- Forward Speed of Car A: 21 km/h (convert to m/s: \( 21 \times \frac{1000}{3600} = 5.83 \) m/s)- Acceleration of Car A: 3.0 m/s²- Radius of Ferris wheel: \( R = 8.4 \) m- Angular rate: \( \Omega = 3.2 \) rev/min (convert to rad/s: \( 3.2 \times \frac{2\pi}{60} = 0.335 \) rad/s)- Angle: 44°### Answers:**Velocity ( \(v_{A/B}\) ):**\[ v_{A/B} = \begin{pmatrix} 3.878 \\ 2.025 \end{pmatrix} \text{ m/s} \]**Acceleration ( \(a_{A/B}\) ):**\[ a_{A/B} = \begin{pmatrix} 3.723 \\ -0.606 \end{pmatrix} \text{ m/s}² \]### Explanation of the Diagram:1. **Ferris Wheel**: The large circle represents the Ferris wheel. The radius of the wheel is labeled as \( R = 8.4 \) m.2. **Car A**: The car is shown on a straight path at the base of the Ferris wheel.3. **Observer B**: Located at an angle of 44° above the horizontal axis on the Ferris wheel.4. **Angular Rate**: Indicated as

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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 = 3.2 rev/min of the Ferris wheel is constant.

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 = 3.2 rev/min of the Ferris wheel is constant.

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### Ferris Wheel Car Problem

**Problem Statement:**

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 non-rotating chair on the Ferris wheel. The angular rate Ω = 3.2 rev/min of the Ferris wheel is constant.

**Diagram:**

![Diagram](image-link)

- The Ferris wheel has a radius \( R = 8.4 \) m.
- The angle at which the observer B is located from the horizontal axis is 44°.
- The Ferris wheel has an angular rate \( \Omega = 3.2 \) rev/min.
- The car A is moving along a straight path on the ground.

**Given:**

- Forward Speed of Car A: 21 km/h (convert to m/s: \( 21 \times \frac{1000}{3600} = 5.83 \) m/s)
- Acceleration of Car A: 3.0 m/s²
- Radius of Ferris wheel: \( R = 8.4 \) m
- Angular rate: \( \Omega = 3.2 \) rev/min (convert to rad/s: \( 3.2 \times \frac{2\pi}{60} = 0.335 \) rad/s)
- Angle: 44°

### Answers:

**Velocity ( \(v_{A/B}\) ):**

\[ v_{A/B} = \begin{pmatrix} 3.878 \\ 2.025 \end{pmatrix} \text{ m/s} \]

**Acceleration ( \(a_{A/B}\) ):**

\[ a_{A/B} = \begin{pmatrix} 3.723 \\ -0.606 \end{pmatrix} \text{ m/s}² \]

### Explanation of the Diagram:

1. **Ferris Wheel**: The large circle represents the Ferris wheel. The radius of the wheel is labeled as \( R = 8.4 \) m.
2. **Car A**: The car is shown on a straight path at the base of the Ferris wheel.
3. **Observer B**: Located at an angle of 44° above the horizontal axis on the Ferris wheel.
4. **Angular Rate**: Indicated as

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