A particle \(P\) of mass 0.8 kg is moving along a straight horizontal line on a smooth hoizontal surface with speed \(4 \mathrm {~ms} ^ { - 1 }\). A second particle \(Q\) of mass 2 kg is moving, in the opposite direction to \(P\), along the same straight line with speed \(2 \mathrm {~ms} ^ { - 1 }\). The particles collide directly. Immediately after the collision the direction of motion of each particle is reversed and the speed of \(P\) is \(2.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
Find the speed of \(Q\) immediately after the collision.
Find the magnitude of the impulse exerted by \(Q\) on \(P\) in the collision, stating the units of your answer.
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Figure 1
A non-uniform plank \(A B\) has weight 60 N and length 5 m . The plank rests horizontally in equilibrium on two smooth supports at \(A\) and \(C\), where \(A C = 3 \mathrm {~m}\), as shown in Figure 1. A parcel of weight 12 N is placed on the plank at \(B\) and the plank remains horizontal and in equilibrium. The magnitude of the reaction of the support at \(A\) on the plank is half the magnitude of the reaction of the support at \(C\) on the plank.
By modelling the plank as a non-uniform rod and the parcel as a particle,
find the distance of the centre of mass of the plank from \(A\).
State briefly how you have used the modelling assumption