Question

(Air Refueling) (ATP- )

For two or more tankers and one receiver (cell). After completion of this refueling, the receiver will descend, then maneuver left (____ or less of heading change), until established in a position ____ below and ____ in trail of the next tanker (as necessary).

Answer 1

The question requires using vector mathematics to calculate the position vectors of two planes based on their climb angles, altitudes, and headings, and then determining the distance between them.

Step-by-step explanation:

The question involves using vector mathematics to determine positions and distances between two aircraft from an air traffic controller's perspective. To find the position vectors of the planes, we need to consider their altitudes and the angles they are climbing at relative to the horizontal, as well as their respective directional headings.

To solve part (a), for the Boeing 747, which is climbing at 10° above the horizontal and heading 30° north of west, we can represent its position relative to the control tower using a three-dimensional vector that has both horizontal and vertical components. Similarly, for the DC-3, climbing at 5° above the horizontal and heading directly west, its position vector would also have horizontal and vertical components corresponding to its climb and direction. These vectors can be calculated using trigonometric functions based on the given angles and altitudes.

For part (b), once we have the position vectors, we would find the distance between the planes by calculating the magnitude of the difference between their position vectors. This can be done using the Pythagorean theorem in three dimensions.