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Forces \(F_{1} = (8N, 030°)\) and \(F_{2} = (10N, 150°)\) act on a particle. Find...

Further Mathematics
WAEC 2015

Forces \(F_{1} = (8N, 030°)\) and \(F_{2} = (10N, 150°)\) act on a particle. Find the horizontal component of the resultant force.

  • A. 1.7N
  • B. 4.5N
  • C. 9.0N
  • D. 13.0N
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Correct Answer: Option A
Explanation

\(F = F \cos \theta + F \sin \theta\)

where \(F \cos \theta = \text{horizontal component}\)

\(F \sin \theta = \text{vertical component}\)

Horizontal component of resultant = sum of horizontal compoents of individual forces

= \(8 \cos 30 + 10 \cos 150 = 6.928 - 8.66 \approxeq - 1.7N\)


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