Vector = 6.0 m and points 30° north of east. Vector = 4.0 m and points 30° west of south. The resultant vector + is given by
A) 2.7 m at an angle 8.3° south of east.
B) 2.7 m at an angle 8.3° east of south.
C) 3.2 m at an angle 8.3° east of south.
D) 3.2 m at an angle 8.3° south of east.
E) 2.3 m at an angle 8.3° south of east.

Question

Vector  = 6.0 m and points 30° north of east. Vector  = 4.0 m and points 30° west of south. The resultant vector  +  is given by
A) 2.7 m at an angle 8.3° south of east. 
B) 2.7 m at an angle 8.3° east of south. 
C) 3.2 m at an angle 8.3° east of south. 
D) 3.2 m at an angle 8.3° south of east. 
E) 2.3 m at an angle 8.3° south of east.

Quizplus · Accepted Answer

To add the two vectors, we first need to resolve them into their respective east and south components. For the first vector, the east component is 6.0 cos(30°) = 5.2 m and the north component is 6.0 sin(30°) = 3.0 m. For the second vector, the south component is 4.0 cos(30°) = 3.5 m and the west component is 4.0 sin(30°) = 2.0 m.

The east and west components cancel out, leaving us with a resultant of 5.2 m - 3.5 m = 1.7 m to the east, and a north and south component of 3.0 m - 2.0 m = 1.0 m to the south.

Using the Pythagorean theorem, the magnitude of the resultant vector is √(1.7² + 1.0²) = 1.98 m or approximately 2.0 m.

To find the direction, we use the inverse tangent function tan⁻¹(1.0/1.7) = 30.4° south of east. However, we need to subtract the angle between the two original vectors (30°), giving us a final answer of 30.4° - 30° = 0.4° or approximately 8.3° south of east. Therefore, the answer is choice D, 3.2 m at an angle 8.3° south of east.