A body is acted upon by two forces \(F_{1} = (5 N, 060°)\) and \(F_{2} = (10 N, 180°)\). Find the magnitude of the resultant force.

A.

18.75 N

B.

15.75 N

C.

9.50 N

D.

8.66 N

Correct answer is D

\(F_{1} = (5 N, 060°) = 5 \cos 60 i + 5 \sin 60 j = 2.5 i + \frac{5\sqrt{3}}{2}j\)

\(F_{2} = (10 N, 180°) = 10 \cos 180 i + 10 \sin 180 j = -10i\)

\(R = F_{1} + F_{2} = -7.5 i + \frac{5\sqrt{3}}{2}j\)

\(|R| = \sqrt{(-7.5)^{2} + (\frac{5\sqrt{3}}{2})^{2}}\)

= \(\sqrt{56.25 + 18.75} = \sqrt{75}\)

= 8.66 N