Anonymous

Velocity and v^2 are both functions of an instantaneous measure. If you want to find a relationship related to the height, you need to work with acceleration.

Anonymous

They can't BOTH be linearly related to height. The correct formula, when there is no friction, is 2hg = v^2, where g is the acceleration of gravity. g = 9.80665 m/s^2, with some variation around the world. So h and v^2 are linearly related.

Anonymous

H = initial height h = height during rolling velocity squared is proportional to H-h (because kinetic energy gained = potential energy lost) so velocity is proportional to square roof of (H-h)

Anonymous

Ball's can not roll w/o friction; it is better stated, in such a question, to "ignore the friction force". Thus the question honors the fact that friction MUST exist and reminds the answerer to not forget this fact. :>)