Question

A plane leaves Seattle, flies 81.0 at 22.0 north of east, and then changes direction to 53.0 south of east. After flying at 122 in this new direction, the pilot must make an emergency landing on a field. The Seattle airport facility dispatches a rescue crew. 1-In what direction should the crew fly to go directly to the field? Use components to solve this problem. 2-How far should the crew fly to go directly to the field? Use components to solve this problem.

Answer 1

Answer:

The crew should fly to go directly to the field to 162.97 units at 24.31° south of east.

Explanation:

We need to find the distance that the plane traveled at east and either north or south so we need to decompose both travels on different axles like: $East = 81*Cos(22)+122*Cos(53) = 75.1+73.42=148.52(units)$ and $South=81*Sin(22)-122*Sin(53)=30.34-97.43=-67.1(units)$. First we use the trigonometric identity Arctan and get the direction:$\alpha =Arctan(\frac{-67.1}{148.52} )=-24.31(degrees)$, then we need to use pythagorean theorem to get how far the crew should fly to the field: $R^{2} =x^{2} +y^{2} =\sqrt{(148.52)^{2} +(-67.1)^{2}} =162.97(units)$