A plane leaves Seattle, flies 85 mi at 22 degree north of east, and then changes

Question

A plane leaves Seattle, flies 85 mi at 22 degree north of east, and then changes direction to 48 degree south of east. After flying at 115 ml in this new direction, the pilot must make an emergency landing on a field. The Seattle airport facility dispatches a rescue crew, (a) In what direction and how far should the crew fly to go directly to the field? Use components to solve this problem. (b) Check the reasonableness of your answer with a careful graphical sum. A plane leaves Seattle, flies 85 mi at 22 degree north of east, and then changes direction to 48 degree south of east. After flying at 115 ml in this new direction, the pilot must make an emergency landing on a field. The Seattle airport facility dispatches a rescue crew, (a) In what direction and how far should the crew fly to go directly to the field? Use components to solve this problem. (b) Check the reasonableness of your answer with a careful graphical sum.

Explanation / Answer

Given
s1 = 85 cos22(i)+ 85 sin 22(j)
s2 = 115 cos48 (i)+ 115 sin (48) (-j)
The distance along x axis is
sx = 85 cos22(i)+ 115 cos48 (i)
= 85 * 0.92 +115 * 0.66 =154.1 (i)
The distance along y axis is
sy = 85 sin 22(j) +115 sin (48) (-j)
= -53.62 (j)
The net displacement is
S = v(154.1)^2 +(53.62 )^2
= 163.16 mi
Direction is
theta =tan^-1(-53.62/154.1) =-19.18 degree

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