# Investigating Motion: Ferris Wheel

Dreamworld is in the process of designing a new ride: The world’s first half underground Ferris Wheel!
• They have constructed a scale model to do testing on and are looking to find a way to graph the height of the car above the ground, given the angle it has travelled around the wheel.
• Riders board the wheel from the right hand side (As seen from the diagram). We are looking to investigate the way in which the height of the car changes depending on the angle around the circle.
Create a triangle using the polygon tool by clicking point A, clicking the car and then by clicking another point below the car on the x axis (This last point should appear as point B). [list=2]
• [/list]Click on the input line at the bottom of the screen. Type B=(x(car),0) into the input line and press enter. This should fix the point B to always move directly underneath the car along the x axis. [list=3]
• [/list]Set the angle from the boarding point by typing θ=angle[C,A,car] into the input bar at the bottom of the screen and pressing ‘enter’. [list=4]
• [/list]Set a point 'S' that is defined by the height of the car at angle θ by typing S=( θ,y(car)) into the input bar and pressing 'enter' [list=5]
• [/list] Move the car around the wheel to see the motion of point S as it maps out the height dependent on the angle. [list=6]
• [/list]Check the 'Show Details' box and the 'Show Trace' to graph height vs. angle by tracing the movement of the point 'S' [list=7]
• [/list]Type the function y= sin(x) into the input bar and observe the relation with the traced trajectory of 'S' [list=8]
• [/list]Uncheck 'Show Trace' and adjust the amplitude slider to see the effects of changing the size of the wheel. [list=9]
• [/list]Trace the graph of height vs. angle for various sizes of the ferris wheel and try to guess the functions that would match by typing them into the input bar.