\begin{enumerate} \item Two particles, \(P\) and \(Q\), of mass 2 kg and 1.5 kg respectively are at rest on a smooth, horizontal surface. They are connected by a light, inelastic string which is initially slack. Particle \(P\) is projected away from \(Q\) with a speed of \(7 \mathrm {~ms} ^ { - 1 }\).

1. Find the common speed of the particles after the string becomes taut.
2. Calculate the impulse in the string when it jerks tight. \item Particle \(A\) has velocity \(( 8 \mathbf { i } - 3 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) and particle \(B\) has velocity \(( 15 \mathbf { i } - 8 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\) where \(\mathbf { i }\) and \(\mathbf { j }\) are perpendicular, horizontal unit vectors.