Launching A Punctiform Object

The net force acting on the object is resultant of $\frac{m \cdot v^2}{R}$ and $m \cdot g$ $\Rightarrow \sqrt{(\frac{m \cdot v^2}{R})^2 + (mg)^2} = \sqrt 17\cdot m \cdot g \Rightarrow v^2 = 4\cdot g\cdot R$ thus from $Work Energy Theorem$ we get the height achieved by the object from point P as $h = 2\cdot R$ So total height achieved by the object is $h + R = 3R$ . We can design the ramp so that object touches the ramp at its heighest point so it gives $h_{max} = 3R$