Answer to Question #139816 in Physics for Jay

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 = 20° to find the magnitude R of the resultant vector and the angle θ that it makes with the +x axis.

Answer 1

As we see, first, we can determine the vertical component of the vector of magnitude 20:

$$|A|=A\text{cos}\phi=20\text{cos}20°=18.8$$

Then, using Pythagorean theorem, find R:

$$R=\sqrt{45^2+18.8^2}=48.8.$$

The angle is

$$\theta=\text{atan}\frac{18.8}{45}=22.8°.$$