An airplane with an airspeed of 120 km/h has a heading of 30° east of north in a wind that is blowing toward the west at 30 km/h. What is the speed of the plane relative to the ground?
A) 150 km/h
B) 90 km/h
C) 140 km/h
D) 110 km/h

Question

Quizplus · Accepted Answer

The plane's velocity relative to the ground is the vector sum of its airspeed and the wind speed. The northward component of the plane's velocity is 120 km/h * cos(30°) = 103.92 km/h, and the eastward component is 120 km/h * sin(30°) = 60 km/h. The wind affects only the east-west component, reducing it by 30 km/h, resulting in a net eastward component of 30 km/h. The ground speed is the magnitude of the resultant vector: √(103.92² + 30²) ≈ 110 km/h.

An Airplane with an Airspeed of 120 Km/h Has a Heading