Final answer:
To find the ground speed and direction of the plane, use vector addition and break down the wind vector into its components. Add the airspeed vector to the wind vector components and find the magnitude and direction of the resultant vector. The correct answer is option (a): Ground Speed = 622.5 mph, Direction = 150°.
Step-by-step explanation:
To find the ground speed and direction of the plane, we need to use vector addition. First, we need to break down the wind vector into its components: north and east. The wind blowing at 50 mph at N30° can be split into 50*sin(30°) mph northward and 50*cos(30°) mph eastward.
Next, we add the airspeed vector (650 mph) to the wind vector components separately. This can be done by adding the north and east components of the vectors. The ground speed is the magnitude of the resultant vector (the sum of the vectors) and can be found using the Pythagorean theorem. The direction of the ground speed can be found by taking the inverse tangent of the north component divided by the east component.
In this case, the ground speed is approximately 622.5 mph and the direction is approximately 150°. Therefore, the correct answer is option (a): Ground Speed = 622.5 mph, Direction = 150°.