Relative velocity: An airplane flies between two points on the ground that are 500 km apart. The destination is directly north of the origination of the flight. The plane flies with an air speed of 120 m/s. If a constant wind blows at 10.0 m/s due west during the flight, what direction must the plane fly relative to north to arrive at the destination?
A) 4.78° east of north
B) 4.76° east of north
C) 85.2° west of north
D) 4.78° west of north
E) 4.76° west of north

Question

Quizplus · Accepted Answer

To arrive directly north at the destination despite the westward wind, the plane must compensate by flying slightly east of north. The angle θ can be found using trigonometry, where tan(θ) = wind speed / plane speed = 10 / 120. Solving for θ gives an angle slightly less than 5° east of north, which matches choice A, 4.78° east of north.

Relative Velocity: an Airplane Flies Between Two Points on the Ground