Question

In going around a storm a plane flies 125 miles south, then 140 miles at 30 degrees south of west, and finally 225 miles at 15 degrees north of west. What is the displacement of the plane from its original position?

Answer 1

365.16 miles

Explanation:

In order to find the displacement, firs find the N/S and E/W displacements individually. Assuming south and west as our positive axes.

`N/S = 125 + 140*sin(30) - 225*sin(15)\\N/S = 136.7657\ miles\\\\E/W = 0 + 140*cos(30) + 225*cos(15)\\E/W = 338.5769`

The displacement of the plane is given by:

`D^2 = (N/S)^2+(E/W)^2\\D=√(136.7657^2+338.5769^2)\\D=365.16\ miles`

The displacement of the plane from its original position is 365.16 miles.