What is the approximate sum of the following two vectors: magnitude 20 at 30 ° and magnitude 10 at 60°?
A) magnitude 29 at 40 °
B) magnitude 30 at 30 °
C) magnitude 30 at 90 °
D) magnitude 40 at 90 °

Question

Quizplus · Accepted Answer

To approximate the sum of the two vectors, we can use vector addition. The first vector can be decomposed into components: $20\cos(30°)$ in the x-direction and $20\sin(30°)$ in the y-direction. The second vector decomposes into $10\cos(60°)$ in the x-direction and $10\sin(60°)$ in the y-direction. Adding these components together and then calculating the magnitude and direction of the resultant vector gives a result closest to the magnitude 29 at 40°.

What Is the Approximate Sum of the Following Two Vectors