Block slides down hemisphere; time to leave surface?

You've obviously got an expression for angular velocity if you've determined "the where." Integrate it.

 

Expanding what Bystander said (in case you're not familiar with angular velocity)
[tex]v=\frac{ds}{dt}=r\frac{d\theta}{dt}[/tex]
in which ds is an increment of arc length. r is, of course, a constant.
You can substitute this value for v into your equation, then separate variables.
If I'm not interested in the challenge of the integration I sometimes use the Wolfram on-line integrator.