A body is acted upon by forces \(F_{1} = (10 N, 090°)\) and \(F_{2} =
FURTHER MATHEMATICS
WAEC 2009
A body is acted upon by forces \(F_{1} = (10 N, 090°)\) and \(F_{2} = (6 N, 180°)\). Find the magnitude of the resultant force.
- A. 11.6 N
- B. 11.7 N
- C. 11.8 N
- D. 11.9 N
Correct Answer: B. 11.7 N
Explanation
\(F = F \cos \theta i + F \sin \theta j\) (Resolving F into its components)
\(F_{1} = (10 N, 090°) = 10 \cos 90 i + 10 \sin 90 j\)
= \(10 j\)
\(F_{2} = (6 N, 180°) = 6 \cos 180 i + 6 \sin 180 j\)
= \(-6 i\)
\(R = - 6 i + 10 j\)
\(|R| = \sqrt{(-6)^{2} + (10)^{2}}\)
= \(\sqrt{136}\)
= 11.7 N
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