7 Two particles \(A\) and \(B\), of masses 0.4 kg and 0.2 kg respectively, are moving down the same line of greatest slope of a smooth plane. The plane is inclined at \(30 ^ { \circ }\) to the horizontal, and \(A\) is higher up the plane than \(B\). When the particles collide, the speeds of \(A\) and \(B\) are \(3 \mathrm {~ms} ^ { - 1 }\) and \(2 \mathrm {~ms} ^ { - 1 }\) respectively. In the collision between the particles, the speed of \(A\) is reduced to \(2.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Find the speed of \(B\) immediately after the collision.
   After the collision, when \(B\) has moved 1.6 m down the plane from the point of collision, it hits a barrier and returns back up the same line of greatest slope. \(B\) hits the barrier 0.4 s after the collision, and when it hits the barrier, its speed is reduced by \(90 \%\). The two particles collide again 0.44 s after their previous collision, and they then coalesce on impact.
2. Show that the speed of \(B\) immediately after it hits the barrier is \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Hence find the speed of the combined particle immediately after the second collision between \(A\) and \(B\).
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