Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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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.
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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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