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\includegraphics[max width=\textwidth, alt={}, center]{ae5d1e27-5853-48aa-9046-86ce1c1a154a-3_149_606_1626_772} Two particles of masses 0.18 kg and m kg move on a smooth horizontal plane. They are moving towards each other in the same straight line when they collide. Immediately before the impact the speeds of the particles are \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) respectively (see diagram).

1. Given that the particles are brought to rest by the impact, find m .
2. Given instead that the particles move with equal speeds of \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) after the impact, find
   (a) the value of m , assuming that the particles move in opposite directions after the impact,
   (b) the two possible values of m , assuming that the particles coalesce.