We appreciate your visit to Part of a railroad track follows a circular arc with a central angle of 28 0 If the radius of the arc of the inner. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To determine how much longer the outer rail of the track is compared to the inner rail, follow these steps:
1. Understand the Scenario:
- You're given a section of a railroad track that forms a circular arc.
- The central angle of this arc is 28.0 degrees.
- The radius of the inner rail is 93.67 feet.
- The distance between the two rails (inner and outer) is 4.71 feet.
2. Convert the Central Angle to Radians:
- Since calculations with arcs often require the angle in radians rather than degrees, we need to convert 28.0 degrees to radians.
- Use the conversion formula: [tex]\( \text{Radians} = \text{Degrees} \times \frac{\pi}{180} \)[/tex].
- Therefore, 28.0 degrees is approximately 0.489 radians.
3. Calculate the Length of the Inner Rail:
- The formula to calculate the length of an arc is [tex]\( \text{Arc length} = \text{Radius} \times \text{Central angle in radians} \)[/tex].
- For the inner rail:
[tex]\[
\text{Length} = 93.67 \, \text{ft} \times 0.489 \approx 45.78 \, \text{ft}
\][/tex]
4. Calculate the Radius of the Outer Rail:
- The outer rail's radius is the inner rail's radius plus the distance between the rails.
- So, the outer radius is [tex]\( 93.67 \, \text{ft} + 4.71 \, \text{ft} = 98.38 \, \text{ft} \)[/tex].
5. Calculate the Length of the Outer Rail:
- Use the arc length formula again for the outer rail:
[tex]\[
\text{Length} = 98.38 \, \text{ft} \times 0.489 \approx 48.08 \, \text{ft}
\][/tex]
6. Find the Difference in Lengths:
- Subtract the length of the inner rail from the length of the outer rail:
[tex]\[
48.08 \, \text{ft} - 45.78 \, \text{ft} \approx 2.30 \, \text{ft}
\][/tex]
Therefore, the outer rail is approximately 2.30 feet longer than the inner rail.
1. Understand the Scenario:
- You're given a section of a railroad track that forms a circular arc.
- The central angle of this arc is 28.0 degrees.
- The radius of the inner rail is 93.67 feet.
- The distance between the two rails (inner and outer) is 4.71 feet.
2. Convert the Central Angle to Radians:
- Since calculations with arcs often require the angle in radians rather than degrees, we need to convert 28.0 degrees to radians.
- Use the conversion formula: [tex]\( \text{Radians} = \text{Degrees} \times \frac{\pi}{180} \)[/tex].
- Therefore, 28.0 degrees is approximately 0.489 radians.
3. Calculate the Length of the Inner Rail:
- The formula to calculate the length of an arc is [tex]\( \text{Arc length} = \text{Radius} \times \text{Central angle in radians} \)[/tex].
- For the inner rail:
[tex]\[
\text{Length} = 93.67 \, \text{ft} \times 0.489 \approx 45.78 \, \text{ft}
\][/tex]
4. Calculate the Radius of the Outer Rail:
- The outer rail's radius is the inner rail's radius plus the distance between the rails.
- So, the outer radius is [tex]\( 93.67 \, \text{ft} + 4.71 \, \text{ft} = 98.38 \, \text{ft} \)[/tex].
5. Calculate the Length of the Outer Rail:
- Use the arc length formula again for the outer rail:
[tex]\[
\text{Length} = 98.38 \, \text{ft} \times 0.489 \approx 48.08 \, \text{ft}
\][/tex]
6. Find the Difference in Lengths:
- Subtract the length of the inner rail from the length of the outer rail:
[tex]\[
48.08 \, \text{ft} - 45.78 \, \text{ft} \approx 2.30 \, \text{ft}
\][/tex]
Therefore, the outer rail is approximately 2.30 feet longer than the inner rail.
Thanks for taking the time to read Part of a railroad track follows a circular arc with a central angle of 28 0 If the radius of the arc of the inner. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
