Question

A plane travels 150 km at 30 degrees NE, turns to go 123 km at 45 degrees SW, then turns one more time 20 degrees SE 325 km. Draw the planes displacements. A calculate the components of each vector

Answer 1

To determine the components of each vector in the plane's displacement, use the cosine function for the horizontal component and the sine function for the vertical component, based on the given angle and magnitude of the vector.

Step-by-step explanation:

The question involves vector components and displacement in plane motion. To find the components of a displacement vector, you can use trigonometric functions based on the given angle and the magnitude of the displacement. Consider a displacement vector D at an angle θ to the horizontal. Its horizontal component, Dx, can be found by Dx = D * cos(θ), and its vertical component, Dy, by Dy = D * sin(θ).

Example Calculation:

• For the first leg: The plane travels 150 km at 30 degrees NE. The components would be: East component (Dx) = 150 km * cos(30º) and North component (Dy) = 150 km * sin(30º).
• For the second leg: The plane travels 123 km at 45 degrees SW, which is equivalent to 45 degrees NW if measured from the south. This leads to: West component (Dx) = 123 km * cos(45º) and South component (Dy) = 123 km * sin(45º).
• For the third leg: The plane travels 325 km at 20 degrees SE. This translates to: East component (Dx) = 325 km * cos(20º) and South component (Dy) = 325 km * sin(20º).