Final answer:
The aircraft is flying northward at 30 km/hr while a westward wind blows at 80 km/hr. The direction of the aircraft over the ground is northwest due to the wind's influence.
Step-by-step explanation:
The direction of the aircraft as it travels over the ground is affected by both its own velocity and the wind's speed and direction. The aircraft is moving northward at 30 km/hr, and the wind is blowing westward at 80 km/hr. To determine the plane's resultant velocity, which gives the direction of travel over the ground, we can use vector addition. Imagine a right triangle where the plane's northward movement is the vertical leg and the wind's westward movement is the horizontal leg. The hypotenuse would then represent the resultant velocity, both in magnitude and direction.
Using the Pythagorean theorem, we find that the magnitude of the resultant velocity is √(30² + 80²) km/hr, which indicates how fast the plane is actually traveling over the ground. However, the direction is the key interest here. The angle of deviation from north (where the wind pushes the plane westward) can be determined using trigonometry, specifically the arctan function. The direction is indeed north-west because the wind is stronger and imposes a greater influence on the plane's trajectory.