A particle $$\(P\)$$ of mass $$\(0.75 \mathrm{~kg}\)$$ is moving along a straight line on a horizontal surface. At the instant when the speed of $$\(P\)$$ is $$\(6 \mathrm{~m} \mathrm{~s}^{-1}\)$$, it receives an impulse of magnitude $$\(\sqrt{24} \mathrm{Ns}\)$$. The impulse acts in the plane of the horizontal surface. At the instant when $$\(P\)$$ receives the impulse, the line of action of the impulse makes an angle of $$\(60^{\circ}\)$$ with the direction of motion of $$\(P\)$$, as shown in Figure 2. Find (i) the speed of $$\(P\)$$ immediately after receiving the impulse, (ii) the size of the angle between the direction of motion of $$\(P\)$$ immediately before receiving the impulse and the direction of motion of $$\(P\)$$ immediately after receiving the impulse. (7)

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