1 A smooth horizontal surface lies in the \(x - y\) plane. A particle \(P\) of mass 0.5 kg is moving on the surface with speed \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the \(x\)-direction when it is struck by a horizontal blow whose impulse has components - 3.5 N s and 2.4 N s in the \(x\)-direction and \(y\)-direction respectively.

1. Find the components in the \(x\)-direction and the \(y\)-direction of the velocity of \(P\) immediately after the blow. Hence show that the speed of \(P\) immediately after the blow is \(5.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
   \(P\) is struck by a second horizontal blow whose impulse is \(\mathbf { I }\).
2. Given that \(P\) 's direction of motion immediately after this blow is parallel to the \(x\)-axis, write down the component of \(\mathbf { I }\) in the \(y\)-direction.