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Answer :
Sure! Let's break down the solution to both parts of the question step by step.
### Part 1: Calculating the Aspect Ratio
1. Understanding Aspect Ratio:
- The aspect ratio of a wing is calculated by dividing the wingspan by the chord. The chord is the width of the wing.
2. Given Data for the First Question:
- Wingspan = 42 feet
- Chord = 84 inches
3. Convert Chord from Inches to Feet:
- Since the wingspan is given in feet, we need to convert the chord from inches to feet.
- To convert inches to feet, divide by 12:
[tex]\[
\text{Chord in feet} = \frac{84 \text{ inches}}{12} = 7 \text{ feet}
\][/tex]
4. Calculate the Aspect Ratio:
- Using the formula:
[tex]\[
\text{Aspect Ratio} = \frac{\text{Wingspan}}{\text{Chord}}
\][/tex]
- Substitute the values:
[tex]\[
\text{Aspect Ratio} = \frac{42 \text{ feet}}{7 \text{ feet}} = 6.0
\][/tex]
### Part 2: Finding the Wingspan from a Given Aspect Ratio
1. Given Data for the Second Question:
- Aspect Ratio = 6:1
- Chord = 6 feet
2. Calculate the Wingspan:
- Rearrange the formula for aspect ratio to find the wingspan:
[tex]\[
\text{Wingspan} = \text{Aspect Ratio} \times \text{Chord}
\][/tex]
- Substitute the values:
[tex]\[
\text{Wingspan} = 6 \times 6 \text{ feet} = 36 \text{ feet}
\][/tex]
So, for the first question, the aspect ratio is 6.0, and for the second question, the wingspan is 36 feet.
### Part 1: Calculating the Aspect Ratio
1. Understanding Aspect Ratio:
- The aspect ratio of a wing is calculated by dividing the wingspan by the chord. The chord is the width of the wing.
2. Given Data for the First Question:
- Wingspan = 42 feet
- Chord = 84 inches
3. Convert Chord from Inches to Feet:
- Since the wingspan is given in feet, we need to convert the chord from inches to feet.
- To convert inches to feet, divide by 12:
[tex]\[
\text{Chord in feet} = \frac{84 \text{ inches}}{12} = 7 \text{ feet}
\][/tex]
4. Calculate the Aspect Ratio:
- Using the formula:
[tex]\[
\text{Aspect Ratio} = \frac{\text{Wingspan}}{\text{Chord}}
\][/tex]
- Substitute the values:
[tex]\[
\text{Aspect Ratio} = \frac{42 \text{ feet}}{7 \text{ feet}} = 6.0
\][/tex]
### Part 2: Finding the Wingspan from a Given Aspect Ratio
1. Given Data for the Second Question:
- Aspect Ratio = 6:1
- Chord = 6 feet
2. Calculate the Wingspan:
- Rearrange the formula for aspect ratio to find the wingspan:
[tex]\[
\text{Wingspan} = \text{Aspect Ratio} \times \text{Chord}
\][/tex]
- Substitute the values:
[tex]\[
\text{Wingspan} = 6 \times 6 \text{ feet} = 36 \text{ feet}
\][/tex]
So, for the first question, the aspect ratio is 6.0, and for the second question, the wingspan is 36 feet.
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