Three forces \(-63j , 32.14i + 38.3j\) and \(14i - 24.25j\) act on a body
FURTHER MATHEMATICS
WAEC 2012
Three forces \(-63j , 32.14i + 38.3j\) and \(14i - 24.25j\) act on a body of mass 5kg. Find, correct to one decimal place, the :
(a) magnitude of the resultant force ;
(b) acceleration of the body.
Explanation
(a) Resultant of forces, \(R = -63j + (32.14i + 38.3j) + (14i - 24.25j)\)
= \(46.14i - 48.95j\)
Magnitude |R| = \(\sqrt{(46.14)^{2} + (-48.95)^{2}}\)
= \(\sqrt{2128.9 + 2396.1}\)
= \(\sqrt{4525}\)
= \(67.268 \approxeq 67.3N\) (to 1 d.p)
(b) \(a = \frac{F}{m}\)
= \(\frac{67.268}{5} = 13.454 ms^{-2}\)
\(\approxeq 13.5 ms^{-2}\)
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