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\includegraphics[max width=\textwidth, alt={}, center]{470e70de-66ba-4dcc-a205-0c92f29471b1-2_227_878_269_635} A particle \(P\) of mass 0.5 kg is travelling with speed \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) on a smooth horizontal plane towards a stationary particle \(Q\) of mass \(m \mathrm {~kg}\) (see diagram). The particles collide, and immediately after the collision \(P\) has speed \(0.8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(Q\) has speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Given that both particles are moving in the same direction after the collision, calculate \(m\).
2. Given instead that the particles are moving in opposite directions after the collision, calculate \(m\).