Final answer:
To determine the relative positions of a Boeing 747 and a Douglas DC-3, one must use trigonometry to calculate their position vectors. Then, the distance between the planes can be found by calculating the magnitude of the difference between these vectors.
Step-by-step explanation:
To answer the student’s question, we must refer to position vectors and geometry to calculate the relative positions of the Boeing 747 and the Douglas DC-3 with respect to the control tower. Note that the specific light signal from a control tower that directs a pilot to taxi is not provided in this question, as it concerns air traffic control rather than the physics of the situation described.
To find the position vectors of the planes, you must consider the altitude, angle above the horizontal, and the direction in which each plane is moving. You can use trigonometry to calculate the horizontal and vertical components of the position vectors. Once you have both position vectors, you can determine the distance between the two planes by finding the magnitude of the difference between these two vectors.
Position Vector Calculation
For Boeing 747:
Vertical component = 2500 m
Horizontal distance = 2500 m / tan(10°)
Direction = 30° north of west
For DC-3:
Vertical component = 3000 m
Horizontal distance = 3000 m / tan(5°)
Direction = directly west
Distance Calculation
The distance between the planes can be calculated by finding the difference between the position vectors and then finding the magnitude of that difference vector.