Final answer:
To handle the scenario of two planes at a regional airport within Class G Airspace, the position vectors are determined using trigonometric functions based on the planes' climb angles and headings, and the distance between them is calculated using vector subtraction and the magnitude of the resulting vector.
Step-by-step explanation:
For the scenario involving the Boeing 747 and the Douglas DC-3, we need to define position vectors and calculate the distance between the two planes from the perspective of an air traffic controller in a control tower at a regional airport. These planes operate in specific patterns and operations within controlled and uncontrolled airspace.
Finding Position Vectors
To find the position vectors relative to the control tower, the given climb angles, and headings for each plane are needed. Considering the climb angles and the direction, we can use trigonometry to calculate the position vectors. For example, if the Boeing 747 is climbing at a 10° angle and moving 30° north of west at an altitude of 2500 m, we can use the sine and cosine functions to determine the components of the position vector.
Calculating the Distance
After determining the position vectors, we calculate the distance between the planes using the Pythagorean theorem or another suitable method of vector subtraction to find the resultant vector, which represents the distance between the two aircraft. This involves subtracting the position vectors of one plane from the other and then calculating the magnitude of the resulting vector.