Analytical Method to Find Plane's Distance and Displacement Vector

How can we use the analytical method to find the plane's straight-line distance from the starting point and the geographic direction of its displacement vector?

By using the analytical method, we can calculate the plane's straight-line distance from the starting point and determine the geographic direction of its displacement vector. Do you want to know how to do it?

When analyzing the plane's flight path, we can break it down into segments and calculate the total displacement to find the distance from the starting point. The analytical method involves determining the coordinates of the final and initial positions of the plane and using trigonometric functions to calculate the total distance traveled.

Straight-Line Distance Calculation:

To find the straight-line distance (d) from the starting point, we utilize the coordinates of the final position after the plane completes its flight path. By applying trigonometry formulas for the x and y coordinates, we can calculate the hypotenuse of the triangle formed by the coordinates.

The straight-line distance formula is: d = sqrt(x1^2 + y1^2)

After calculation, we find that the plane's straight-line distance is 64.1 km.

Geographic Direction of Displacement Vector:

The displacement vector's geographic direction is determined by the angle that the distance forms with the east axis. By calculating the tangent of this angle using the y and x coordinates, we can find the direction of the displacement vector.

The formula for calculating the angle θ is: tanθ = y1/x1

After calculation, we find that the geographic direction of the displacement vector is 36.4º North of East (counterclockwise from the east axis).