Child sliding down a frictionless slide

[jfreimer]

Homework Statement

A child starts from rest and slides down a frictionless slide. In terms of R and H,
at what height h will he lose contact with the section of radius R?

(child starts at the top with height H, at the bottom the slide flattens out and then forms a quarter circle to the ground with radius R)

Homework Equations

The Attempt at a Solution

I tried figuring it out using potential energy and kinetic energy since that is the chapter. I think it has something to do with mgH=mgh+1/2mv^2 and then solving v^2 for some value using centripetal motion but I wasn't sure how to set that step up.

 

[Gib Z]

I had you attempt at a solution in mind as well. Equating Potential Energies and solving. Now, what is the equation for Centripetal Force?

$$F=\frac{mv^2}{r}$$

Just work from there.

 

[atat1tata]

My attempt for a solution has given the answer h=2H/3 if R >=2H/3 , else h=R
Is it possible?