Vector = 6.0 m and points 30° south of east. Vector = 4.0 m and points 30° south of west. The resultant vector + is given by
A) 3.3 m at an angle 71° south of east.
B) 5.3 m at an angle 71° south of east.
C) 3.3 m at an angle 19° south of east.
D) 5.3 m at an angle 19° south of east.
E) 2.6 m at an angle 19° south of east.

Question

Vector  = 6.0 m and points 30° south of east. Vector  = 4.0 m and points 30° south of west. The resultant vector  +  is given by
A) 3.3 m at an angle 71° south of east. 
B) 5.3 m at an angle 71° south of east. 
C) 3.3 m at an angle 19° south of east. 
D) 5.3 m at an angle 19° south of east. 
E) 2.6 m at an angle 19° south of east.

Quizplus · Accepted Answer

To find the resultant vector, we need to add the two given vectors. First, we can find the components of each vector in the horizontal and vertical directions.

Vector 11ea6ebb_72cb_ccf7_9d78_b754b5d47a66_TB6213_11:
Horizontal component = 6.0*cos(30°) = 5.2 m
Vertical component = 6.0*sin(30°) = 3.0 m

Vector 11ea6ebb_72cb_ccf8_9d78_297a003d6940_TB6213_11:
Horizontal component = -4.0*cos(30°) = -3.5 m
Vertical component = 4.0*sin(30°) = 2.0 m

Next, we can add the horizontal and vertical components separately to get the components of the resultant vector.

Horizontal component of resultant vector = 5.2 - 3.5 = 1.7 m
Vertical component of resultant vector = 3.0 + 2.0 = 5.0 m

Finally, we can use the Pythagorean theorem and inverse tangent function to find the magnitude and direction of the resultant vector.

Magnitude of resultant vector = sqrt((1.7)^2 + (5.0)^2) = 5.3 m
Direction of resultant vector = atan(5.0/1.7) = 71° south of east

Therefore, the answer is B.