A particle is thrown as shown in the figure . It hits a smooth inclined plane at a point A. If the maximum height attained by the particle can be represented as \(\dfrac{a}{b}\) where a and b are co-prime integers. Then what is the value of \(a+b\)

**Details and assumptions:**

\(\bullet\)The distance OP is \(\dfrac{10}{3}\) m

\(\bullet\)\(u = 5\sqrt5 m/s\)

\(\bullet\)\(\beta\) \(=\)\(37^{\circ}\)

\(\bullet\)\(\alpha = tan^{-1}(0.5)\)

\(\bullet\)\(g = 10m/s^2\)

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