Find the sum of two vectors if one has a direction of 52° and a magnitude of 12 and the other has a direction of 30° and a magnitude of 8.
A)magnitude of 19.65 with a direction of 46.8°
B)magnitude of 19.65 with a direction of 41°
C)magnitude of 19.65 with a direction of 43.2°
D)magnitude of 14.42 with a direction of 41°

Question

Quizplus · Accepted Answer

To find the sum of two vectors, we can use the component method. 
The first vector has a direction of 52° and magnitude of 12. We can find its horizontal and vertical components: 
$V_{1x}=12\cos(52°)≈7.68$ 
$V_{1y}=12\sin(52°)≈9.24$

Similarly, the second vector has a direction of 30° and magnitude of 8. 
$V_{2x}=8\cos(30°)≈6.93$ 
$V_{2y}=8\sin(30°)≈4$

The sum of the two vectors is then: 
$V_{x}=V_{1x}+V_{2x}≈14.61$ 
$V_{y}=V_{1y}+V_{2y}≈13.24$

The magnitude of the sum vector is: 
$|V|=√(V_{x}^2+V_{y}^2)≈19.65$

The direction can be found using: 
$	heta=tan^{−1}(V_{y}/V_{x})≈43.2°$

Therefore, the answer is C.

Find the Sum of Two Vectors If One Has a Direction