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WAEC Further Mathematics 2015 Question 21

Question 21

Statics

Forces of magnitude 8 N and 5 N act on a body as shown in the diagram. Calculate, correct to 2 decimal places, the resultant force acting at O.

Diagram for this question
  1. A.14.06 N
  2. B.13.00 N
  3. C.9.83 N
  4. D.8.26 N
Show the answer and explanation

Answer: D (8.26 N)

Explanation

Horizontal: 8 cos 45° − 5 cos 30° = 5.657 − 4.330 = 1.327; vertical: 8 sin 45° + 5 sin 30° = 5.657 + 2.5 = 8.157. Resultant = √(1.327² + 8.157²) ≈ 8.26 N.