(a)

A carousel angle of rotation is .

It totates feet from the center of the carousel, .

If is a central angle in a circle of radius , then the length of the intercepted arc is given by .

Convert to radian measure.

Substitute and in .

The distance between  rider to the center of the carousel is ft.

(b)

Since rider seated  feet from the center of the carousel, .

Substitute and in .

The distance between  rider to the center of the carousel is ft.

The difference in the carousel ditances is .

(a) The distance between  rider to the center of the carousel is ft.

(b) The difference in the carousel ditances is ft.