Vector
Has a magnitude of 8.0 m and points 30° north of east;vector
Has a magnitude of 6.0 m and points 30° west of north;and vector
Has a magnitude of 5.0 m and points 30° west of south.The resultant vector
+
+
Is given by
A)2.7 m at an angle 74° north of east.
B)5.9 m at an angle 74° north of east.
C)4.8 m at an angle 74° east of north.
D)5.1 m at an angle 74° north of east.
E)2.1 m at an angle 66° east of north.

Question

Vector 
Has a magnitude of 8.0 m and points 30° north of east;vector 
Has a magnitude of 6.0 m and points 30° west of north;and vector 
Has a magnitude of 5.0 m and points 30° west of south.The resultant vector 
+ 
+ 
Is given by
A)2.7 m at an angle 74° north of east. 
B)5.9 m at an angle 74° north of east. 
C)4.8 m at an angle 74° east of north. 
D)5.1 m at an angle 74° north of east. 
E)2.1 m at an angle 66° east of north.

Quizplus · Accepted Answer

First, we need to resolve the three given vectors into their x and y components:
Vector 1 (8.0 m, 30° north of east):
x-component: 8.0 cos(30°) = 6.93 m
y-component: 8.0 sin(30°) = 4.00 m
Vector 2 (6.0 m, 30° west of north):
x-component: 6.0 sin(30°) = 3.00 m (note the negative because it's pointing to the left)
y-component: 6.0 cos(30°) = 5.20 m
Vector 3 (5.0 m, 30° west of south):
x-component: 5.0 sin(30°) = 2.50 m (note the negative because it's pointing to the left)
y-component: -5.0 cos(30°) = -4.33 m (note the negative because it's pointing down)

Next, we add up the x and y components separately:
x-component: 6.93 m + 3.00 m + 2.50 m = 12.43 m
y-component: 4.00 m + 5.20 m - 4.33 m = 4.87 m

Finally, we use the Pythagorean theorem and inverse tangent to find the magnitude and angle of the resultant vector:
Magnitude: sqrt((12.43 m)^2 + (4.87 m)^2) = 13.14 m
Angle: tan^-1(4.87 m / 12.43 m) = 21.77°
Since the resultant vector is pointing to the northeast quadrant, we need to add 90° to get the final angle measurement:
Final angle: 21.77° + 90° = 111.77°
Rounding to one significant figure gives 110°, which is closest to the answer choice D: 5.1 m at an angle 74° north of east.

Vector Has a Magnitude of 8.0 M and Points 30° North