A Ferris wheel completes 7 revolutions in 14 minutes. The radius of the Ferris wheel is 30 feet. What is the linear velocity of the Ferris wheel in inches per second?
A Ferris wheel completes 7 revolutions in 14 minutes. The radius of the Ferris wheel is 30 feet. What is the linear velocity of the Ferris wheel in inches per second?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Linear Velocity of a Ferris Wheel Calculation**
A Ferris wheel completes 7 revolutions in 14 minutes. The radius of the Ferris wheel is 30 feet.
**Question:**
What is the linear velocity of the Ferris wheel in inches per second?
Enter your answer, rounded to the nearest tenth, in the box below:
**Input Box:**
```
| 18.9 | inches per second
```
**Explanation:**
To find the linear velocity, we first need to convert the given measurements and apply the appropriate formula for linear velocity.
1. **Convert the radius to inches:**
- Radius (r) = 30 feet = 30 * 12 inches = 360 inches
2. **Calculate the circumference (C) of the Ferris wheel:**
- Circumference \( C = 2 \pi r = 2 \pi \times 360 \) inches ≈ 2261.95 inches
3. **Find the time in seconds:**
- Time (T) = 14 minutes = 14 * 60 seconds = 840 seconds
4. **Calculate the total distance traveled in 7 revolutions:**
- Distance traveled = 7 revolutions * 2261.95 inches ≈ 15833.65 inches
5. **Compute the linear velocity (v):**
- Linear velocity \( v = \frac{{\text{Distance}}}{{\text{Time}}} = \frac{{15833.65 \, \text{inches}}}{{840 \, \text{seconds}}} \approx 18.86 \, \text{inches per second}\)
Rounding to the nearest tenth:
- **Linear velocity**: 18.9 inches per second
This concludes that the linear velocity of the Ferris wheel, rounded to the nearest tenth, is 18.9 inches per second.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fd604ca-8dc6-4a27-ba35-1469eb31e622%2F8b4ce699-0b59-4125-8627-0b7c25d95ea9%2Fswe4q0y_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Linear Velocity of a Ferris Wheel Calculation**
A Ferris wheel completes 7 revolutions in 14 minutes. The radius of the Ferris wheel is 30 feet.
**Question:**
What is the linear velocity of the Ferris wheel in inches per second?
Enter your answer, rounded to the nearest tenth, in the box below:
**Input Box:**
```
| 18.9 | inches per second
```
**Explanation:**
To find the linear velocity, we first need to convert the given measurements and apply the appropriate formula for linear velocity.
1. **Convert the radius to inches:**
- Radius (r) = 30 feet = 30 * 12 inches = 360 inches
2. **Calculate the circumference (C) of the Ferris wheel:**
- Circumference \( C = 2 \pi r = 2 \pi \times 360 \) inches ≈ 2261.95 inches
3. **Find the time in seconds:**
- Time (T) = 14 minutes = 14 * 60 seconds = 840 seconds
4. **Calculate the total distance traveled in 7 revolutions:**
- Distance traveled = 7 revolutions * 2261.95 inches ≈ 15833.65 inches
5. **Compute the linear velocity (v):**
- Linear velocity \( v = \frac{{\text{Distance}}}{{\text{Time}}} = \frac{{15833.65 \, \text{inches}}}{{840 \, \text{seconds}}} \approx 18.86 \, \text{inches per second}\)
Rounding to the nearest tenth:
- **Linear velocity**: 18.9 inches per second
This concludes that the linear velocity of the Ferris wheel, rounded to the nearest tenth, is 18.9 inches per second.
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