1 A particle \(P\) of mass 0.2 kg is moving on a smooth horizontal surface with speed \(3 \mathrm {~ms} ^ { - 1 }\), when it is struck by an impulse of magnitude \(I\) Ns. The impulse acts horizontally in a direction perpendicular to the original direction of motion of \(P\), and causes the direction of motion of \(P\) to change by an angle \(\alpha\), where \(\tan \alpha = \frac { 5 } { 12 }\).
- Show that \(I = 0.25\).
- Find the speed of \(P\) after the impulse acts.