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Concept explainers
Uniform Motion A Cessna (heading south at
Find parametric equations that model the motion of the Cessna and the
Find a formula for the distance between the planes as a function of time.
Graph the function in part (b) using the graphing utility.
What is the minimum distance between the planes? When are the planes closest?
Simulate the motion of the planes by simultaneously graphing the equations found in part (a).
(a)
![Check Mark](/static/check-mark.png)
The parametric equation that model of the Cessna and the Boeing
Answer to Problem 58AYU
Solution:
The parametric equation of the Cessna is
Explanation of Solution
Given information:
A Cessna (heading south at
Explanation:
Let the motion of Cessna be
A Cessna and a Boeing
So the sign of distance is negative.
Here, the
The heading speed of Cessna along
The heading speed of Cessna along
The heading speed of the Boeing
The heading speed of the Boeing
The initial distance of Cessna from the point the intersection is
The distance from the point of intersection is equal to the initial distance plus the product of speed and time
The parametric equation that models the motion of the Cessna and the Boeing
The parametric equation that models the motion of the Cessna is
The parametric equation that models the motion of the Cessna is
Thus, the parametric equation of the Cessna is
(b)
![Check Mark](/static/check-mark.png)
The formula for distance between the planes as a function of time.
Answer to Problem 58AYU
Solution:
The formula for distance between the planes is
Explanation of Solution
Given information:
A Cessna (heading south at
Explanation:
The positions of the flight form a right angle triangle.
Let
To find the distance between the two planes by using the Pythagorean Theorem, Here,
By using the Pythagorean Theorem
Thus, the distance between the two planes is
(c)
![Check Mark](/static/check-mark.png)
To graph: The function in part (b) using the graphing utility.
Explanation of Solution
Given information:
The function of time is
Graph:
Step I: Press the ON key.
Step II: Now, press [Y=]. Input the right hand side of the function
Step IV: Press [WINDOW] key, and set the viewing window as below:
Step IV: Then hit [Graph] key to view the graph.
Interpretation:
Distance between Cessna and Boeing 737 decreases and then increases.
(d)
![Check Mark](/static/check-mark.png)
The minimum distance between the planes and time when the planes are closest.
Answer to Problem 58AYU
Solution:
The minimum distance between the planes is
Explanation of Solution
Given information:
A Cessna (heading south at
Explanation:
The function for distance between the planes is
To find the minimum distance between the planes by using graphing utility, Step I: Press the ON key.
Step II: Now, press [Y=]. Input the right hand side of the function
Step IV: Press [WINDOW] key, and set the viewing window as below:
Step IV: Then hit [Graph] key to view the graph.
Step V: Press [2nd] [TRACE] to access the calculate menu.
Step VI: Press [3] to the minimum.
Step VII: If necessary, repeatedly press the up-down arrow keys until the appropriate function appears in the border at the top of the screen.
Step VIII: Set the left bound of the minimum point.
Step IX: Set the right bound of the minimum point.
Step X: Press the Enter twice for the minimum point.
From the above graph, the minimum distance between the planes is
(e)
![Check Mark](/static/check-mark.png)
To graph: The Simulate motion of the planes by simultaneously graphing the equation found in part (a).
Explanation of Solution
Given information:
A Cessna (heading south at
Graph:
From part (a),
Parametric equations to describe the Cessna motion and the Boeing
Cessna:
Boeing
From part (d),
The planes are closest at
In parametric mode with
For
The relative position of Cessna and Boeing
The relative positions of Cessna and Boeing
The relative positions of Cessna and Boeing
The relative positions of Cessna and Boeing
The relative positions of Cessna and Boeing
Interpretation:
The graphs show the relative positions of Cessna and Boeing
Chapter 10 Solutions
Precalculus
Additional Math Textbook Solutions
Precalculus Enhanced with Graphing Utilities (7th Edition)
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