Here’s a challenge physics question, which you can solve with a working knowledge of first-year college physics (even of the non-Calculus variety), but which you might find a bit tricky. I will post the answer in a week or two.

A small object slides frictionlessly from the top of a hemisphere of radius *R*. (The size of the object is much less than *R*.) It will slide along the hemisphere for a while, but at some point it will fly off of the hemisphere.

First question: at what position does the small object leave the sphere? You can give this answer by giving the angle *θ* shown on the picture above where the small object leaves the sphere.

Second question: what distance *d* does the object land away from the edge of the sphere?

Answers should be in terms of *R*, the radius of the sphere, and *g*, the gravity of earth.

If you want to visualize what’s happening, here’s a quick simulation I rendered using Blender’s physics engine.

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