Answer to Question #125186 in Physics for randal

Question

Given are the vectors A = 30 N 45 N of W and B = 45 N 75 S of E. Determine a) their resultant and in Newtons

Answer 1

The resultant of the vectors is denoted as C on the figure below

The magnitude of the resultant can be found in the following way. First, notice, that angle opposite to the C is equal to 30 degrees. Then let's apply the law of cosines to the triangle ABC. Obtain:

$$C^2 = A^2 + B^2 - 2AB\cos30\degree = 30^2 + 45^2 - 2\cdot 30\cdot45\cdot \dfrac{\sqrt{2}}{2} \approx 1015.8$$

Thus,

$$C = \sqrt{1015.8}\approx 31.87N$$

Answer. 31.87 N.