Some amusement parks have a double Ferris wheel, which consists of two vertically rotating wheels that are attached to each other by a bar that also rotates. There are eight gondolas equally spaced on each wheel. Riders experience a combination of two circular motions that provide a sensation more thrilling than the classic single Ferris wheel. In particular, riders experience the greatest sensation when their rate of change in height is the greatest. . Each of the two wheels is 6 m in diameter and revolves every 12 s. . The rotating bar is 9 m long. The ends of the bar are attached to the centres of the wheels. . The height from the ground to the centre of the bar is & m. The bar makes a complete revolution every 20 s. A rider starts seated at the lowest position and moves counterclockwise. . The bar starts in the vertical position. Consider the height of a rider who begins the ride in the lowest car.f] Design your own double Ferris wheel. Determine the position function for a rider on your wheel. What is the maximum speed experienced by your riders? Is there a simple relationship between the dimensions of the Ferris wheel and the maximum heights or speeds experienced