An observer stands 20 m from the bottom of a Ferris wheel on a line that is perpendicular to the face of the wheel, with her eyes at the level of the bottom of the wheel. The wheel revolves at a rate of \(\pi\) rad/min and the observer's line of sight with a specific seat on the Ferris wheel makes an angle \(\theta\) with the horizontal (see figure). At what time during a full revolution is \(\theta\) changing most rapidly?

Solution 43E Step 1: Consider that an observer stands 20 m from the bottom of the Ferris wheel on a line that is perpendicular to the face of the wheel. Consider the line with observer sight and a seat makes angle and the line length is L m. Now, consider the diameter of the wheel is r m. Also, consider that the radius of the wheel is r m. Now, the revolving rate is So, the height of the seat from the ground is: Here t is the time in minute. Draw the wheel accordingly