The McDonnell Douglas (now Boeing) F-15E Strike Eagle is an American all-weather multirole strike fighter derived from the McDonnell Douglas F-15 Eagle. The F-15E was designed in the 1980s for long-range, high-speed interdiction without relying on escort or electronic-warfare aircraft. The F- 15E is flying horizontally at an altitude of 3 miles and at a speed of 480 mph passes directly above an observer on the ground. How fast is the distance from the observer to the airplane increasing 30 seconds later? Show all your work. Give units. 3 mi Observer Ground
The McDonnell Douglas (now Boeing) F-15E Strike Eagle is an American all-weather multirole strike fighter derived from the McDonnell Douglas F-15 Eagle. The F-15E was designed in the 1980s for long-range, high-speed interdiction without relying on escort or electronic-warfare aircraft. The F- 15E is flying horizontally at an altitude of 3 miles and at a speed of 480 mph passes directly above an observer on the ground. How fast is the distance from the observer to the airplane increasing 30 seconds later? Show all your work. Give units. 3 mi Observer Ground
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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![### Q8
**Description:**
The McDonnell Douglas (now Boeing) F-15E Strike Eagle is an American all-weather multirole strike fighter derived from the McDonnell Douglas F-15 Eagle. The F-15E was designed in the 1980s for long-range, high-speed interdiction without relying on escort or electronic-warfare aircraft. The F-15E is flying horizontally at an altitude of 3 miles and at a speed of 480 mph while passing directly above an observer on the ground.
**Question:**
How fast is the distance from the observer to the airplane increasing 30 seconds later? Show all your work. Give units.
**Diagram Explanation:**
The accompanying diagram illustrates the scenario as follows:
- The F-15E fighter jet is depicted in horizontal flight at a constant altitude of 3 miles above the ground.
- An observer is positioned vertically below the aircraft at ground level.
- The distance from the observer to the ground is denoted to be 3 miles.
- The aircraft's horizontal displacement is represented by an arrow pointing to the right, indicating its velocity.
In this scenario, we are asked to calculate the rate at which the distance between the observer and the airplane increases after 30 seconds.
Here is how to approach the solution:
1. **Determine the horizontal distance traveled in 30 seconds:**
\[
\text{Distance} = \text{speed} \times \text{time}
\]
Given the speed is 480 mph, and time is 30 seconds,
Convert 30 seconds to hours:
\[
t = \frac{30 \text{ seconds}}{3600 \text{ seconds/hour}} = \frac{1}{120} \text{ hours}
\]
Now, calculate the horizontal distance:
\[
d = 480 \text{ mph} \times \frac{1}{120} \text{ hours} = 4 \text{ miles}
\]
2. **Calculate the total distance from the observer to the airplane:**
Using the Pythagorean theorem for the right triangle formed by the horizontal and vertical distances:
\[
\text{Total distance} = \sqrt{(\text{horizontal distance})^2 + (\text{altitude})^2}
\]
Substitute the known values:
\[
\text{Total distance} = \sqrt](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2cc04b1e-803c-4d9d-b550-d2ae04bcc2b3%2Fbb49bbe2-7fb6-4d82-9605-f35318f00a30%2Fjc7pel6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Q8
**Description:**
The McDonnell Douglas (now Boeing) F-15E Strike Eagle is an American all-weather multirole strike fighter derived from the McDonnell Douglas F-15 Eagle. The F-15E was designed in the 1980s for long-range, high-speed interdiction without relying on escort or electronic-warfare aircraft. The F-15E is flying horizontally at an altitude of 3 miles and at a speed of 480 mph while passing directly above an observer on the ground.
**Question:**
How fast is the distance from the observer to the airplane increasing 30 seconds later? Show all your work. Give units.
**Diagram Explanation:**
The accompanying diagram illustrates the scenario as follows:
- The F-15E fighter jet is depicted in horizontal flight at a constant altitude of 3 miles above the ground.
- An observer is positioned vertically below the aircraft at ground level.
- The distance from the observer to the ground is denoted to be 3 miles.
- The aircraft's horizontal displacement is represented by an arrow pointing to the right, indicating its velocity.
In this scenario, we are asked to calculate the rate at which the distance between the observer and the airplane increases after 30 seconds.
Here is how to approach the solution:
1. **Determine the horizontal distance traveled in 30 seconds:**
\[
\text{Distance} = \text{speed} \times \text{time}
\]
Given the speed is 480 mph, and time is 30 seconds,
Convert 30 seconds to hours:
\[
t = \frac{30 \text{ seconds}}{3600 \text{ seconds/hour}} = \frac{1}{120} \text{ hours}
\]
Now, calculate the horizontal distance:
\[
d = 480 \text{ mph} \times \frac{1}{120} \text{ hours} = 4 \text{ miles}
\]
2. **Calculate the total distance from the observer to the airplane:**
Using the Pythagorean theorem for the right triangle formed by the horizontal and vertical distances:
\[
\text{Total distance} = \sqrt{(\text{horizontal distance})^2 + (\text{altitude})^2}
\]
Substitute the known values:
\[
\text{Total distance} = \sqrt
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