Question

A plane has an eastward heading with an airspeed of 156 m/s. A 20.0 m/s wind is blowing southward at the same time as the plane is flying. The velocity of the plane relative to the ground is A) 157 m/s at an angle 7.31° south of east.

B) 157 m/s at an angle 7.31° east of south.
C) 155 m/s at an angle 7.36° south of east.
D) 155 m/s at an angle 7.36° east of south.
E) 157 m/s at an angle 7.36° south of east.

Answer 1

The velocity of the plane relative to the ground is 157 m/s at an angle 7.31° south of east.

Step-by-step explanation:

The velocity of the plane relative to the ground can be found by vector addition. The eastward heading of the plane and its airspeed can be represented as a vector with magnitude 156 m/s and direction due east. The southward wind can be represented as a vector with magnitude 20.0 m/s and direction due south.

To find the velocity of the plane relative to the ground, we add the vectors representing the plane's heading and the wind. Using vector addition, we can find the resultant magnitude and direction. Considering the eastward heading and the southward wind, the resultant velocity of the plane relative to the ground is 157 m/s at an angle 7.31° south of east. Therefore, the correct answer is option A) 157 m/s at an angle 7.31° south of east.