Watching A Ferris Wheel Problem
I am totally lost in my calculus class and I am supposed to show the class how to work this problem and it's due Friday!!! I have no idea what to do!(Crying) An observer stands 20m 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. At what time during a full revolution is theta changing most rapidly?
Re: Watching A Ferris Wheel Problem
Let r be the radius of the ferris wheel. Then you should be able to find an expression for the height of the seat being observed as a function of time. It will also give you the distance from the center line, and from that and 20m you can get an expression for the horizontal distance to the seat being observed. Then you can finally get theta as a function of time, so you take the derivative and set it to zero.
If I understand the problem correctly, the angle theta is between the line of sight and the horizontal plane, i.e. how far it is above the horizon, ignoring the side-to-side motion, so the diagram is a little deceptive.