Question

A marble with radius r rolls in an L-shaped track. How far is the center of the marble from the corner of the track?

Answer 1

r√2

Explanation:

You want to know the distance from the center of a marble of radius r to the corner of an L-shaped track in which it rolls.

Center

The center of the marble can only come within r of the track edges, so the distance to the corner will be the hypotenuse of a right triangle with legs r. That distance is r√2.

The center of the marble is r√2 from the corner of the track.

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Additional comment

You can see in the second attachment that the distance to the corner of the track will depend on where the marble is rolling in the track. It might only be r away from the corner.

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