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[In this question, i and j are horizontal unit vectors] A particle P of mass 4kg is at rest at the point A on a smooth horizontal plane. At time i: 0, two forces, F1 = (4i j)N and F2 = (ii + yj)N, Where A and y are constants, are applied to P Given that P moves in the direction of the vector (3i + j) (a) show that A3y+7=0 At time t: 4 seconds, P passes through the point B. Given that A = 2 (b) nd the length of AB. Figure 2 A uniform rod AB has mass M and length 2a A particle of mass 2M is attached to the red at the point C, where AC = 1.5a The rod rests with its end A on rough horizontal ground. The rod is held in equilibrium at an angle 6' to the ground by a light string that is attached to the end B of the rod. The string is perpendicular to the rod, as shown in Figure 2. (a) Explain why the frictional force acting on the red at A acts horizontally to the right on the diagram. The tension in the string is T (b) Show that T = 2Mg cos 9 3 Given that cos 6 = E (c) show that the magnitude of the vertical force exerted by the ground on the red at A 57Mg 25 is The coefcient of friction between the rod and the ground is ,u Given that the rod is in limiting equilibrium, 8 d h tht = ()sow an 19