The fixed point $$\(A\)$$ is $$\(h\)$$ metres vertically above the point $$\(O\)$$ that is on horizontal ground. At time $$\(t=0\)$$, a particle $$\(P\)$$ is projected from $$\(A\)$$ with speed $$\(10 \mathrm{~m} \mathrm{~s}^{-1}\)$$. The particle moves freely under gravity. At time $$\(t=2.5\)$$ seconds, $$\(P\)$$ strikes the ground at the point $$\(B\)$$. At the instant when $$\(P\)$$ strikes the ground, the speed of $$\(P\)$$ is $$\(18 \mathrm{~ms}^{-1}\)$$, as shown in Figure 4. (a) By considering energy, find the value of $$\(h\)$$. (3) (b) Find the distance $$\(O B\)$$. (5) As $$\(P\)$$ moves from $$\(A\)$$ to $$\(B\)$$, the speed of $$\(P\)$$ is less than or equal to $$\(8 \mathrm{~m} \mathrm{~s}^{-1}\)$$ for $$\(T\)$$ seconds. (c) Find the value of $$\(T\)$$ (6)

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