Particles A and B, of masses 2.4 kg and 3.3 kg respectively, are connected by a light inextensible string that passes over a smooth pulley which is fixed to the top of a rough plane. The plane makes an angle of θ with horizontal ground. Particle A is on the plane and the section of the string between A and the pulley is parallel to a line of greatest slope of the plane. Particle B hangs vertically below the pulley and is 1 m above the ground (see diagram). The coefficient of friction between the plane and A is μ.

\((a) It is given that θ = 30 and the system is in equilibrium with A on the point of moving directly up the plane.\)

\(Show that μ = 1.01 correct to 3 significant figures.\)

\((b) It is given instead that θ = 20 and μ = 1.01. The system is released from rest with the string taut.\)

Find the total distance travelled by A before coming to instantaneous rest. You may assume that A does not reach the pulley and that B remains at rest after it hits the ground.