Question

In the control tower at a regional airport, an air traffic controller monitors two aircraft as their positions change with respect to the control tower. One plane is a cargo carrier Boeing 747 and the other plane is a Douglas DC-3. The Boeing is at an altitude of 2500 m, climbing at 10° above the horizontal, and moving 30° north of west. The DC-3 is at an altitude of 3000 m, climbing at 5° above the horizontal, and cruising directly west.

a) Position vectors: Boeing - (-2500ˆi + 4330ˆj)m, DC-3 - (3000ˆi)m
b) Position vectors: Boeing - (-2500ˆi + 4330ˆj)m, DC-3 - (3000ˆi + 400ˆj)m
c) Position vectors: Boeing - (2500ˆi + 4330ˆj)m, DC-3 - (-3000ˆi)m
d) Position vectors: Boeing - (2500ˆi + 4330ˆj)m, DC-3 - (-3000ˆi + 400ˆj)m

Answer 1

The question involves using vector operations to determine the position vectors of two aircraft and the distance between them. It requires additional calculations based on the provided angles, altitude, and specific direction of movement, which are not given, making it impossible to select a definitive answer or complete the calculation.

Step-by-step explanation:

The question requires us to use vector operations to determine the positions of two aircraft from a control tower and calculate the distance between them using their positional vectors. We assume east as the positive x-axis direction, north as the positive y-axis, and the altitude as the z-axis component in formulating these position vectors for the Boeing 747 and the Douglas DC-3 aircraft.

To find the position vector of the Boeing 747, we need to convert its movement described as 30° north of west and its climb at an angle of 10° above the horizontal into vector components. Since the Boeing is moving 30° north of west, we can represent the west component as negative on the x-axis and the north component as positive on the y-axis. The climb of 10° above the horizontal translates to a z-component. However, mathematical computation is necessary to determine the accurate vector components based on the given angles and altitude.

For the DC-3, which cruises directly west and climbs at 5° above the horizontal, the position vector would primarily have a negative x-component (since west is opposite to east) and a positive z-component due to the climb, but without calculation, it is not possible to confirm the exact measures.

Therefore, without additional information such as the horizontal distances or speeds of the aircraft, we cannot definitively select one of the given options for the position vectors or calculate the distance between the two planes.