Trig

posted by Lisa

A ferris wheel has a 14 meter diameter and turns counterclockwise at 6 rpm.

a) Assuming that the center of the wheel is the origin of an x-y coordinate plane, write functions to find the position (x,y) of a rider that starts at the bottom of the wheel.
b) Where is the rider 2 minutes after the start of the ride?
c) When does the rider first reach the top of the wheel?
d) How often does the rider reach the top of the wheel?
e) The bottom of the ferris wheel is 1 meter from the ground. Graph the function that represents the height of the rider from the ground at each moment t. (Use the function for the y-coordinate of the rider that you found in part 'a' and adjust it as necessary)

  1. Steve

    period = 10 seconds

    a)
    y = -7cos(2πx/10) = -7cos(πx/5)

    b)
    y(2) = -7cos(2π/5) = -2.16

    c)
    half-period = 5 seconds, x=5

    d)
    rider reaches top once every period - every 10 seconds

    e)
    Just add the wheel radius+1 to the function to get

    h(x) = y(x) + 8 = 8 - 7cos(πx/5)

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