Question

An airplane flies due south at 175 km/h relative to the air. There is a wind blowing at 85 km/h to the east relative to the ground. What is the plane's direction relative to the ground?

A. 50° S of E
B. 64° S of E
C.45º E of S
D.55° W of N
E. 58° N of W

Answer 1

The angle from the resultant vector shows that the correct option is 64° S of E. So, the correct option is B.

Step-by-step explanation:

The student's question involves determining the plane's direction relative to the ground, taking into account the airplane's speed and the wind's effect. The velocity of the airplane southward is 175 km/h, and the wind is blowing to the east at 85 km/h. To solve this, vector addition is required. We need to find the resultant vector of two perpendicular vectors: the plane's southward velocity and the wind's eastward velocity. Using the Pythagorean theorem, we find the magnitude of the plane's ground speed is the square root of the sum of the squares of the southward and eastward components (175 km/h and 85 km/h, respectively). This gives us the plane's speed relative to the ground.

To find the direction, we calculate the angle using the tangent function: tan(theta) = opposite/adjacent, where opposite is the wind speed and adjacent is the plane's speed. The angle is then calculated using the inverse tangent function, tan(theta) = 85/175. With this information, we can conclude that the correct option is B. 64° S of E. This is because the arc tangent of (85/175) is approximately 25.8°, which when subtracted from 90° (to adjust to the correct quadrant) gives approximately 64.2°.