NECO 2023 · Paper 2 · Q7

Statics: forces, equilibrium & moments

Three men pushed a bus with forces of 204 N in the direction $030^\circ$ , 300 N in the direction $090^\circ$ and 225 N in the direction $120^\circ$ . Find the magnitude of the resultant force, correct to the nearest newton.

Worked solution (try it first)

East parts: $204\sin30^\circ + 300\sin90^\circ + 225\sin120^\circ = 102 + 300 + 194.86$
$= 596.86$ .
North parts: $204\cos30^\circ + 300\cos90^\circ + 225\cos120^\circ = 176.67 + 0 - 112.5$
$= 64.17$ .
$R = \sqrt{596.86^2 + 64.17^2}$
$= \sqrt{360\,360}$
$\approx 600\text{ N}$ .

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