Concept explainers
An air-traffic controller observes two aircraft on his radar screen. The first is at altitude 800 m, horizontal distance 19.2 km, and 25.0° south of west. The second aircraft is at altitude 1 100 m, horizontal distance 17.6 km, and 20.0° south of west. What is the distance between the two aircraft? (Place the x axis west, the y axis south, and the z axis vertical.)
The distance between the two aircraft.
Answer to Problem 3.54AP
The distance between the two aircraft is
Explanation of Solution
Given info: The air traffic controller observes two aircraft on his radar screen. The first is at altitude
Consider the
Figure (1)
The displacement vector of the first aircraft in the
Here,
Substitute
Thus, the displacement vector of the first aircraft in
The displacement vector of the first aircraft in the
Here,
Substitute
Thus, the displacement vector of the first aircraft in
The displacement vector of the first aircraft in the
Here,
Substitute
Thus, the displacement vector of the first aircraft in
The position vector of the first aircraft is,
Here,
Substitute
Thus, the position vector of the first aircraft is
The displacement vector of the second aircraft in the
Here,
Substitute
Thus, the displacement vector of the second aircraft in
The displacement vector of the second aircraft in the
Here,
Substitute
Thus, the displacement vector of the second aircraft in
The displacement vector of the second aircraft in the
Here,
Substitute
Thus, the displacement vector of the second aircraft in
The position vector of the second aircraft is,
Here,
Substitute
Thus, the position vector of the second aircraft is
The net distance vector between the two aircraft is,
Here,
Substitute
Thus, the net distance vector between the two aircraft is
The magnitude for the net distance vector between the two aircraft is,
Here,
Substitute
Conclusion:
Therefore, the distance between the two aircraft is
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