6 Particle \(P\) of mass 0.3 kg and particle \(Q\) of mass 0.2 kg are 3.6 m apart on a smooth horizontal surface. \(P\) and \(Q\) are simultaneously projected directly towards each other along a straight line. Before the particles collide \(P\) has speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(Q\) has speed \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Given that the particles coalesce in the collision, calculate their common speed after they collide.
2. It is given instead that one particle is at rest immediately after the collision.
   (a) State which particle is in motion after the collision and find the speed of this particle.
   (b) Find the time taken after the collision for the moving particle to return to its initial position.
   (c) On a single diagram sketch the \(( t , v )\) graphs for the two particles, with \(t = 0\) as the instant of their initial projection.
   \(7 \quad A\) and \(B\) are two points on a line of greatest slope of a plane inclined at \(45 ^ { \circ }\) to the horizontal and \(A B = 2 \mathrm {~m}\). A particle \(P\) of mass 0.4 kg is projected from \(A\) towards \(B\) with speed \(5 \mathrm {~ms} ^ { - 1 }\). The coefficient of friction between the plane and \(P\) is 0.2 .
3. Given that the level of \(A\) is above the level of \(B\), calculate the speed of \(P\) when it passes through the point \(B\), and the time taken to travel from \(A\) to \(B\).
4. Given instead that the level of \(A\) is below the level of \(B\),
   (a) show that \(P\) does not reach \(B\),
   (b) calculate the difference in the momentum of \(P\) for the two occasions when it is at \(A\).