Two forces (2i - 5j)N and (-3i + 4j)N act on a body of mass 5kg. Find in \(ms^{-2}\), the magnitude of the acceleration of the body.

  • A \(\frac{\sqrt{2}}{5}\)
  • B \(5\sqrt{2}\)
  • C \(2\sqrt{5}\)
  • D \(\frac{5\sqrt{2}}{2}\)
waec 2010furthermathematics

The correct answer is A. \(\frac{\sqrt{2}}{5}\)

\(F = F_{1} + F_{2}\)

\((2i - 5j) + (-3i + 4j) = (-i - j)\)

\(F = ma \implies (-1, -1) = 5a\)

\(a = (-\frac{1}{5}, -\frac{1}{5})\)

\(|a| = \sqrt{(\frac{-1}{5})^2 + (\frac{-1}{5})^2} = \sqrt{2}{25}\)

\(|a| = \frac{\sqrt{2}}{5} ms^{-2}\)

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