How are the velocity and velocity^2 of a ball rolling down an incline related to its height and are they linearly related to the height?

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.

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, which is a CHANGE in velocity over a measure of time.

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)

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. :>)

m*g*h = 0.7*m*V^2

mass m cross

V^2 = g*h/0.7 ≈ 14.0*h

V = √g*h/0.7 ≈ 3.74*√h

V^2 is related to the height through a constant which, on earth, is worth ≈ 14.0, while V is related to the square root of height through a constant which, on earth, is worth ≈ 3.74