The pilot of an aircraft flies due north relative to the ground in a wind blowing 40 km/h toward the east. If his speed relative to the ground is 80 km/h, what is the speed of his airplane relative to the air?
A) 89 km/h
B) 85 km/h
C) 81 km/h
D) 76 km/h
E) 72 km/h

Question

Quizplus · Accepted Answer

The speed of the airplane relative to the air can be found using the Pythagorean theorem, considering the northward speed (80 km/h) and the eastward wind speed (40 km/h) as perpendicular components of the airplane's velocity relative to the air. Thus, the airplane's speed relative to the air is $\sqrt{80^2 + 40^2} = \sqrt{6400 + 1600} = \sqrt{8000} = 89.44$ km/h, which rounds to 89 km/h.

The Pilot of an Aircraft Flies Due North Relative to the Ground