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\includegraphics[max width=\textwidth, alt={}, center]{14403602-94a6-4441-a673-65f9b98180e5-2_385_741_269_701} A particle \(P\) of mass 0.5 kg is moving in a straight line with speed \(6.3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). An impulse of magnitude 2.6 N s applied to \(P\) deflects its direction of motion through an angle \(\theta\), and reduces its speed to \(2.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) (see diagram). By considering an impulse-momentum triangle, or otherwise,

1. show that \(\cos \theta = 0.6\),
2. find the angle that the impulse makes with the original direction of motion of \(P\).