Question

A plane flies 34 km [30o W of N] and after a brief stopover flies 58 km [40o E of N]. Determine the plane’s displacement.

Answer 1

To determine the plane's displacement, we need to break down the two legs of the journey into their horizontal and vertical components.

For the first leg of the journey:
- Horizontal component = 34 km * cos(30o) = 34 km * (sqrt(3)/2) ≈ 29.48 km westward
- Vertical component = 34 km * sin(30o) = 34 km * (1/2) = 17 km northward

For the second leg of the journey:
- Horizontal component = 58 km * cos(40o) = 58 km * (3/5) ≈ 34.8 km eastward
- Vertical component = 58 km * sin(40o) = 58 km * (4/5) = 46.4 km northward

Now, we can add up the horizontal and vertical components of both legs of the journey to find the total displacement:
- Horizontal displacement = 29.48 km eastward - 34.8 km westward = -5.32 km westward
- Vertical displacement = 17 km northward + 46.4 km northward = 63.4 km northward

Therefore, the plane's total displacement is 5.32 km westward and 63.4 km northward. This can be represented as a vector with a magnitude of approximately 64.1 km and a direction of approximately 81.78° north of east.