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.\\
(i) 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 $\mathbf { I }$.\\
(ii) 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.

\hfill \mbox{\textit{OCR M3 2008 Q1 [6]}}