1
\includegraphics[max width=\textwidth, alt={}, center]{e004bbb5-f9e1-4ea2-8357-39db9392cb8c-2_355_572_260_788} A particle \(P\) of mass 0.3 kg is moving in a straight line with speed \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) when it is deflected through an angle \(\theta\) by an impulse of magnitude \(I\) N s. The impulse acts at right angles to the initial direction of motion of \(P\) (see diagram). The speed of \(P\) immediately after the impulse acts is \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Show that \(\cos \theta = 0.8\) and find the value of \(I\).