Vector
Has a magnitude of 6.0 m and points 30° north of east.Vector
Has a magnitude of 4.0 m and points 30° east of north.The resultant vector
+
Is given by
A)0.70 m at an angle of 42° north of east.
B)14 m at an angle of 42° north of east.
C)1.1 m at an angle of 42° north of east.
D)9.7 m at an angle of 42° north of east.
E)2.0 m at an angle of 42° north of east.

Question

Vector 
Has a magnitude of 6.0 m and points 30° north of east.Vector 
Has a magnitude of 4.0 m and points 30° east of north.The resultant vector 
+ 
Is given by
A)0.70 m at an angle of 42° north of east. 
B)14 m at an angle of 42° north of east. 
C)1.1 m at an angle of 42° north of east. 
D)9.7 m at an angle of 42° north of east. 
E)2.0 m at an angle of 42° north of east.

Quizplus · Accepted Answer

To find the resultant vector, we need to add the two given vectors:
11ea6c4e_001c_af5d_9875_6ffbd3f29d53_TB6214_11 = 6.0 m at an angle of 30° north of east
11ea6c4e_001c_af5e_9875_39f4f4a7736c_TB6214_11 = 4.0 m at an angle of 30° east of north

Using vector addition, we get:
Resultant vector = √(6.0^2 + 4.0^2 + 2(6.0)(4.0)cos(120°)) = 9.7 m
To find the direction, we use tanθ = (ΣVy/ ΣVx) = (6.0 sin30° + 4.0 sin60°)/ (6.0 cos30° + 4.0 cos60°)
This gives θ = 42° north of east.

Therefore, the best choice is D.

Vector Has a Magnitude of 6.0 M and Points 30° North