Answer to Question #126831 in Classical Mechanics for shyline

Question

Two vectors of magnitude F and 2F have a resultant 1.5F. Calculate the angle between the vectors

Answer 1

The Cosine Rule says

$$(1.5F)^2=F^2+(2F)^2-2F(2F)\cos\theta$$

Hence

$$2.25=1+4-4\cos\theta$$

$$\cos\theta=0.6875$$

$$\theta=46.6^{\circ}$$