Question

A plane leaves Seattle, flies 85 miles at 30° north of east, and then changes direction to 45° south of east. After flying 115 miles in this new direction, the pilot must make an emergency landing in a field. The Seattle airport dispatches a rescue crew. In what direction and how far should the crew fly to go directly to the field? a) b) Check your answer with a careful graphical sum.

Answer 1

Position of seattle = 0i + 0j x_1 = 85 cos 30 degree = 73.61 mi y_1 = 85 sin 30 degree = 42.5 mj New position = (73.61) i + (42.5)j x_2 = 115 cos 45 degree = 81.31i y_2 = 115 sin 45 degree = 81.31j New position = (73.61 + 81.31) i + (42.5 - 81.31)j 154.92i - 38.81j d cos theta = 154.92 d sin theta = -38.81 d = squareroot (154.92)^2 + (38.81)^2 = 159.7 mi theta = tan^-1 (- 38.81/154.92) = -14.06 degree New direction = 14.06 degree so E distance = 159.7 mi