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9709 P42 - Nov 2014 - Q2
3690

Three coplanar forces act at a point. The magnitudes of the forces are 20 N, 25 N, and 30 N, and the directions in which the forces act are as shown in the diagram, where \(\sin \alpha = 0.28\) and \(\cos \alpha = 0.96\), and \(\sin \beta = 0.6\) and \(\cos \beta = 0.8\).

(i) Show that the resultant of the three forces has a zero component in the \(x\)-direction.

(ii) Find the magnitude and direction of the resultant of the three forces.

(iii) The force of magnitude 20 N is replaced by another force. The effect is that the resultant force is unchanged in magnitude but reversed in direction. State the magnitude and direction of the replacement force.

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