A force 10N acts in the direction 060° and another force 6N acts in the...
FURTHER MATHEMATICS
WAEC 2016
A force 10N acts in the direction 060° and another force 6N acts in the direction 330°. Find the y component of their resultant force.
- A. \((3 + 3\sqrt{3})N\)
- B. \((-3 + 5\sqrt{3})N\)
- C. \((5 + 3\sqrt{3})N\)
- D. \((5 + 5\sqrt{3})N\)
Correct Answer: B. \((-3 + 5\sqrt{3})N\)
Explanation
\(F = F\cos \theta + F\sin \theta\) (Resolving into its components)
\(10N = 10 \cos 60, 10 \sin 60\)
\(6N = 6 \cos 330, 6 \sin 330\)
\(R = F_{1} + F_{2} = (10 \cos 60, 10 \sin 60) + (6 \cos 330, 6 \sin 330)\)
The y- component : \(10 \sin 60 + 6 \sin 330 = 10 \times \frac{\sqrt{3}}{2} + 6 \times \frac{-1}{2}\)
= \((5\sqrt{3} - 3)N\)
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