Unit 2 Assignment: The Ferris Wheel

Assignment Objectives In this assignment, you will use some of the fallowing unit objectives: About radians, a method for measuring angles = About the unit circle with a radius of one. * How to prove trigonometric identities. * How tofind the angle when you know a ratio and solve trigonometric functions. * How to graph a trigonometric function and find the amplitude, phase shift, and period. Assignment Introduction The first Ferris Wheel was built in 1893 for the world's fair in Chicago, lllinois. Since then engineers have sought to make them larger and stronger. Currently, the largest Ferris Wheel is the High Roller in Las Vagas, Nevada. A Ferris Wheel (FW) is a classic example of a periodic trigonometric function. This Unit 2 Assignment has two parts that need to be completed by the student. In Part 1, you are given specific dimensions and rotation speed of a Ferris Wheel that you need to use to model the motion of the FW and make a graph of at least one complete rotation of the FW. In Part 2, you are asked to design your own Ferris Wheel, determining diameter, center height from the ground, and speed of rotation. You will then need to write the trigonometric function for the height of the FW as a function of time. Part 1 - Suppose a Ferris Wheel has a diameter of 30 meters, the center is 19 meters off the ground and it makes 2 revolutions per minute (2 rpm). Make a drawing of this W, labeling the diameter or radius, center height off the ground, and the number of rotations per minute. Supposing the minimum height of the FW oceurs when t=0, write the sinuseidal function for the height as a function of time. Make sure to SHOW how you calculated the various constants in your motion equation with some explanation. Lastly, graph the function on a coordinate plane (do not submit a digital calculator graph or one made using computer sofoware), showing at least one complete rotation of the FW, graphing height as a function of time. On your graph, label the coordinates of key points including the maximum and minimurn heights Part 2 - Design your own Ferris Whel, stating diameter, center height offthe ground and the number of rotations per minute. Make a drawing of your FW, labeling the diameter or radius, center height off the ground, and the number of rotations per minute. Again, supposing the minimum height of the FW occurs when t=0, write the sinusoidal funetion for the height as a function of time. Make sure to SHOW how you calculated the various constants in your motion equation with some explanation. Write the function for the height of the Ferris Wheel as a function of time. You DO NOT need to make a graph for Part 2 of the assignment. Finally, write a Reflection Statement about your Unit 2 Assignment experience. What did you learn from doing this assignment? In Part 2, is your Ferris Wheel realistic? Does it travel too fast or too slow? Any other comments or ebservations? Additional Helpful Hints & Tips. = When writing a sinusoidal function to model circular mation, you can use either the sine or cosine functions to model this motion. The initial starting position of the object in motion at time t=0 is a key consideration when deciding which trigonometric function, sine or cosine, to use to model this motion. When making your graphin Part 1, make sure to label the axes with units being used and use sppropriate scales for your data. Before submitting your wark for grading, always take the time to carefully review the instructions in this document and look at the Grading Rubric provided to make sure that you have completed all required tasks and to see how the assignment will be graded. Product to be Submitted This Unit 2 Assignment has two parts that need to be completed by the student. In Part 1, you need to draw a diagram of the given Ferris Wheel showing key dimensions of diameter, center height off the ground, and speed of rotation. You then need to develop a motion equation for the FW based on the given data. And then you need to construct a graph of your FW showing at least one complete rotation of the height versus time, labeling the coordinates of key points including the maximum and minimum heights. In Part 2, you need to design your own Ferris Wheel. You need to draw a diagram of your FW showing key dimensions of diameter, center height off the ground, and speed of rotation. You then need to develop a motion equation for your FW based on your data. You do NOT need to make a graph for Part 2