13. Please calculate the distance in meters of the following stadia images with a k=100. The scale of the target is in decimeters. Note that 1 meter = 10 decimeters E15 F HY+CH E EB F
13. Please calculate the distance in meters of the following stadia images with a k=100. The scale of the target is in decimeters. Note that 1 meter = 10 decimeters E15 F HY+CH E EB F
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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### Distance Calculation Using Stadia Images
**Problem Statement:**
13. Please calculate the distance in meters of the following stadia image with a k=100. The scale of the target is in decimeters. Note that 1 meter = 10 decimeters.
**Description of Graph/Diagram:**
The diagram is an image of a stadia rod viewed through a telescope. The stadia rod is marked in red and black, with major markings at each decimeter increment (such as 13, 14, and 15), and smaller red marks at each tenth of a decimeter.
**Calculation Steps:**
1. **Observation:** The difference in readings between the top stadia hair and the bottom stadia hair is observed. In this image, the top stadia hair appears to be at 15 decimeters and the bottom stadia hair at 13 decimeters.
2. **Calculate the Stadia Interval:**
\[
\text{Stadia Interval} = \text{Top Stadia Hair Reading} - \text{Bottom Stadia Hair Reading}
\]
\[
\text{Stadia Interval} = 15 \text{ dm} - 13 \text{ dm} = 2 \text{ dm}
\]
3. **Convert the Stadia Interval to Meters:**
\[
\text{Stadia Interval in Meters} = \frac{2 \text{ dm}}{10} = 0.2 \text{ m}
\]
4. **Apply the Stadia Constant (k):**
\[
\text{Distance (D)} = \text{k} \times (\text{Stadia Interval})
\]
Given \( k = 100 \),
\[
\text{Distance (D)} = 100 \times 0.2 \text{ m} = 20 \text{ m}
\]
**Conclusion:**
The distance to the target is 20 meters.
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F93c89597-7ce2-4451-bd61-6716aa1c2201%2F6a7a6f16-0945-431c-8dcb-9d58dc87ce03%2Fgkffldn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Distance Calculation Using Stadia Images
**Problem Statement:**
13. Please calculate the distance in meters of the following stadia image with a k=100. The scale of the target is in decimeters. Note that 1 meter = 10 decimeters.
**Description of Graph/Diagram:**
The diagram is an image of a stadia rod viewed through a telescope. The stadia rod is marked in red and black, with major markings at each decimeter increment (such as 13, 14, and 15), and smaller red marks at each tenth of a decimeter.
**Calculation Steps:**
1. **Observation:** The difference in readings between the top stadia hair and the bottom stadia hair is observed. In this image, the top stadia hair appears to be at 15 decimeters and the bottom stadia hair at 13 decimeters.
2. **Calculate the Stadia Interval:**
\[
\text{Stadia Interval} = \text{Top Stadia Hair Reading} - \text{Bottom Stadia Hair Reading}
\]
\[
\text{Stadia Interval} = 15 \text{ dm} - 13 \text{ dm} = 2 \text{ dm}
\]
3. **Convert the Stadia Interval to Meters:**
\[
\text{Stadia Interval in Meters} = \frac{2 \text{ dm}}{10} = 0.2 \text{ m}
\]
4. **Apply the Stadia Constant (k):**
\[
\text{Distance (D)} = \text{k} \times (\text{Stadia Interval})
\]
Given \( k = 100 \),
\[
\text{Distance (D)} = 100 \times 0.2 \text{ m} = 20 \text{ m}
\]
**Conclusion:**
The distance to the target is 20 meters.
---
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