Launching A Punctiform Object

Classical Mechanics Level 3

Consider a circular path of radius \(R\), when passing through the point \(P\) the magnitude of the resultant force on the object is \(\sqrt{17}\text{ mg}\), where \(g\) is the acceleration of gravity.

Find the maximum height \(h_{\text{max}}\) that the object reaches the ramp in terms of \(R\).