A classical mechanics problem by Pankaj Joshi

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

$\bullet$ $u = 5\sqrt5 m/s$

$\bullet$ $\beta$ $=$ $37^{\circ}$

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

$\bullet$ $g = 10m/s^2$