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WAEC Further Mathematics 2022 Question 37

Question 37

Statics

A particle is acted upon by forces F = (10 N, 060°), P = (15 N, 120°) and Q = (12 N, 200°). Express the force that will keep the particle in equilibrium in the form xi + yj, where x and y are scalars.

  1. A.17.55i + 13.78j
  2. B.17.55i − 13.78j
  3. C.−17.55i + 13.78j
  4. D.−17.55i − 13.78j
Show the answer and explanation

Answer: C (−17.55i + 13.78j)

Explanation

With i east and j north, a force (F, θ) is F sin θ i + F cos θ j. The resultant is 17.55i − 13.78j, so the equilibrant is −17.55i + 13.78j.