Final answer:
To determine the magnitude and direction of the plane's resultant velocity, vector addition involving the Pythagorean theorem and arctan function is used, resulting in a magnitude of approximately 232 km/hr and a direction east of north, which is closest to option C.
Step-by-step explanation:
The subject of this question is resultant velocity, which involves vector addition to find the overall effect of two separate velocity vectors: one due to the plane's motion, and one due to the wind. Here, we are dealing with a physics problem that requires an understanding of vector components and trigonometry to find the magnitude and direction of the resultant velocity vector for the plane.
To calculate the magnitude of the resultant vector, we use the Pythagorean theorem since the velocities are perpendicular to one another:
- Resultant speed (R) = √(plane speed² + wind speed²) = √(225 km/hr)² + (55 km/hr)² = √50625 + 3025 = √53650 = 231.63 km/hr, which we round to 232 km/hr (approx).
To find the direction, we calculate the angle using the inverse tangent function, since we have a right triangle:
- Angle (θ) = arctan(wind speed / plane speed) = arctan(55/225)
Angles are typically measured from the north direction in navigation, so the resultant direction is east of north.
The correct answer is therefore close to option C (though the exact magnitude calculated here is 232 km/hr and not 242 km/hr), and the direction is east of north.