Falling sphere in Newton's drag-law region, a sphere initially at rest at z = 0 falls under the influence of gravity. Conditions are such that, after a negligible interval, the sphere falls with a resisting force proportional to the square of the velocity.

(a) Find the distance z that the sphere falls as a function of t.

(b) What is the terminal velocity of the sphere? Assume that the density of the fluid is much less than the density of the sphere.