Answer to Question #95885 in Physics for jamal

Question

The displacement vectors A and B, when added together, give the resultant vector R, so that R = A + B. Use the data in the drawing and the fact that φ = 28° to find the magnitude R of the resultant vector and the angle θ that it makes with the +x axis.

Answer 1

$$R=\sqrt{6^2+8^2+2(6)(8)\cos{(90+28)\degree}}=7.4$$

We have:

$$8\cos{28\degree}=7.4\cos{\theta}$$

$$\theta=\arccos{0.9545}=17\degree$$