You spot a plane that is 1.63 km north, 2.3 km east, and at an altitude 5.2 km above your position.
1) At what angle from due north (in the horizontal plane) are you looking?
( ) °E of N
2) Determine the plane's position vector (from your location) in terms of the unit vectors, letting ihatbold be toward the east direction, jhatbold be toward the north direction, and khatbold be in vertically upward.
( ) km ihatbold
3) ( ) km jhatbold
On this, first compute the bearing based on N. Theta=arctan(E/N). If it had been some west, or S distance, you would use a negative.
Positon vector, you have the N, E vectors, and now, then k= 5.2
so you have N, E, k
1. Tan A = X/Y = 2.3/1.63 = 1.41104.
A =
To answer these questions, we'll need to use vector components and trigonometry.
1) To find the angle from due north, we can use trigonometry. We have the north and east distances, so we can use the arctan function to find the angle.
angle = arctan(east distance / north distance)
In this case, the east distance is 2.3 km and the north distance is 1.63 km.
angle = arctan(2.3 km / 1.63 km)
Using a calculator, we find that the angle is approximately 51.1°. However, since the question asks for the angle in the east direction from due north, we need to subtract this angle from 90°.
angle from due north = 90° - 51.1°
Therefore, the answer to question 1 is approximately 38.9°E of N.
2) The position vector of the plane can be found by combining the north, east, and altitude components:
position vector = north component * jhatbold + east component * ihatbold + altitude component * khatbold
In this case, the north component is 1.63 km, the east component is 2.3 km, and the altitude component is 5.2 km.
position vector = 1.63 km * jhatbold + 2.3 km * ihatbold + 5.2 km * khatbold
So the answer to question 2 is:
(2.3 km * ihatbold)
3) The position vector only has a north component (jhatbold) and an altitude component (khatbold). The plane is not moving in the east direction, so the east component is 0.
position vector = north component * jhatbold + east component * ihatbold + altitude component * khatbold
In this case, the north component is 1.63 km and the altitude component is 5.2 km.
position vector = 1.63 km * jhatbold + 0 * ihatbold + 5.2 km * khatbold
So the answer to question 3 is:
(1.63 km * jhatbold)