An airplane flies at an altitude of 5 miles toward a point directly over an observer. Consider and x as shown in the following figure.
An airplane flies at an altitude of 5 miles toward a point directly over an observer. Consider and x as shown in the following figure.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![# Analyzing the Flight Path
## Problem Statement
An airplane flies at an altitude of 5 miles toward a point directly over an observer. Consider \( \theta \) and \( x \) as shown in the following figure.
## Diagram Explanation
The diagram illustrates a right triangle where:
- The airplane is flying at a constant altitude of 5 miles, represented as the vertical side of the triangle.
- \( x \) denotes the horizontal distance from the observer to the point directly beneath the airplane.
- \( \theta \) is the angle of elevation from the observer's viewpoint to the airplane.
### Tasks:
**(a)** Write \( \theta \) as a function of \( x \).
\[ \theta(x) = \_\_\_\_\_ \]
**(b)** The speed of the plane is 314 miles per hour. Find \( \frac{d\theta}{dt} \) (in rad/h) when \( x = 10 \) and \( x = 5 \). (Round your answers to three decimal places.)
- when \( x = 10 \)
\[ \frac{d\theta}{dt} = \_\_\_\_\_ \text{ rad/h} \]
- when \( x = 5 \)
\[ \frac{d\theta}{dt} = \_\_\_\_\_ \text{ rad/h} \]
### Need Help?
- **Read It**
- **Master It**
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Transcribed Image Text:# Analyzing the Flight Path
## Problem Statement
An airplane flies at an altitude of 5 miles toward a point directly over an observer. Consider \( \theta \) and \( x \) as shown in the following figure.
## Diagram Explanation
The diagram illustrates a right triangle where:
- The airplane is flying at a constant altitude of 5 miles, represented as the vertical side of the triangle.
- \( x \) denotes the horizontal distance from the observer to the point directly beneath the airplane.
- \( \theta \) is the angle of elevation from the observer's viewpoint to the airplane.
### Tasks:
**(a)** Write \( \theta \) as a function of \( x \).
\[ \theta(x) = \_\_\_\_\_ \]
**(b)** The speed of the plane is 314 miles per hour. Find \( \frac{d\theta}{dt} \) (in rad/h) when \( x = 10 \) and \( x = 5 \). (Round your answers to three decimal places.)
- when \( x = 10 \)
\[ \frac{d\theta}{dt} = \_\_\_\_\_ \text{ rad/h} \]
- when \( x = 5 \)
\[ \frac{d\theta}{dt} = \_\_\_\_\_ \text{ rad/h} \]
### Need Help?
- **Read It**
- **Master It**
(Submit your answer through the provided input fields.)
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