5 Two particles \(P\) and \(Q\) are projected vertically upwards from horizontal ground at the same instant. The speeds of projection of \(P\) and \(Q\) are \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(7 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) respectively and the heights of \(P\) and \(Q\) above the ground, \(t\) seconds after projection, are \(h _ { P } \mathrm {~m}\) and \(h _ { Q } \mathrm {~m}\) respectively. Each particle comes to rest on returning to the ground.

1. Find the set of values of \(t\) for which the particles are travelling in opposite directions.
2. At a certain instant, \(P\) and \(Q\) are above the ground and \(3 h _ { P } = 8 h _ { Q }\). Find the velocities of \(P\) and \(Q\) at this instant.