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\includegraphics[max width=\textwidth, alt={}, center]{c0f31235-80aa-4838-844f-b706de55e7cd-2_285_1096_255_488} A particle \(P\) of mass 0.3 kg is moving with speed \(0.4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in a straight line on a smooth horizontal surface when it is struck by a horizontal impulse. After the impulse acts \(P\) has speed \(0.6 \mathrm {~ms} ^ { - 1 }\) and is moving in a direction making an angle \(30 ^ { \circ }\) with its original direction of motion (see diagram).

1. Find the magnitude of the impulse and the angle its line of action makes with the original direction of motion of \(P\). Subsequently a second impulse acts on \(P\). After this second impulse acts, \(P\) again moves from left to right with speed \(0.4 \mathrm {~ms} ^ { - 1 }\) in a direction parallel to its original direction of motion.
2. State the magnitude of the second impulse, and show the direction of the second impulse on a diagram.