Final answer:
To calculate the plane's displacement from the point of lift-off, decompose its movement during ascent at a 45° angle for 2.5 km and then at a 25° angle for 5.2 km into horizontal and vertical components, and then use vector addition or the Pythagorean theorem to find the resultant displacement.
Step-by-step explanation:
The displacement of the plane from the point of lift-off can be calculated by analyzing its movement in two stages with different flight angles. During the first stage, the plane ascends at a 45° angle and travels 2.5 km, while in the second stage, it changes its angle to 25° and covers a distance of 5.2 km.
To find the displacement, we can decompose these movements into their horizontal (x-axis) and vertical (y-axis) components and then use the Pythagorean theorem or vector addition to determine the resultant vector from the origin. Given the provided angles and distances, trigonometric functions like sine and cosine will be employed to find these components.
For the first stage, we can calculate the horizontal and vertical displacements using cosine and sine functions respectively:
Horizontal (x1) = 2.5 km × cos(45°)
Vertical (y1) = 2.5 km × sin(45°)
For the second stage, we use the same approach:
Horizontal (x2) = 5.2 km × cos(25°)
Vertical (y2) = 5.2 km × sin(25°)
The total horizontal and vertical displacements are the sum of the respective stages:
Total horizontal displacement (X) = x1 + x2
Total vertical displacement (Y) = y1 + y2
Finally, the resultant displacement (D) from the point of lift-off is given by:
Displacement (D) = √(X² + Y²)