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: D
Explanation
\(F_{1} = (5 N, 060°) = 5 \cos 60 i + 5 \sin 60 j = 2.5 i + \frac{5\sqrt{3}}{2}j\)
\(F_{2} = (10 N, 180°) = 10 \cos 180 i + 10 \sin 180 j = -10i\)
\(R = F_{1} + F_{2} = -7.5 i + \frac{5\sqrt{3}}{2}j\)
\(|R| = \sqrt{(-7.5)^{2} + (\frac{5\sqrt{3}}{2})^{2}}\)
= \(\sqrt{56.25 + 18.75} = \sqrt{75}\)
= 8.66 N
