Question 1173712
The general form for the height of the Ferris wheel as a function of time is:
h(t) = Acos(wt) + h0, where h0 is the midline, A is the amplitude, and w = the angular speed in radians per minute. 
h(t) oscillates about the midline with an amplitude equal to the radius of the wheel. 
The midline, i.e. halfway up, is given by the radius plus h0 = 19.5 m
Thus the amplitude is equal to 17.5 m. Since the initial height must be 2 m, 
we have A = -17.5. The angular speed is 2*pi radians per 6 min = pi/3 rad/min.
Thus the equation describing the height is h(t) = -17.5*cos((pi/3)*t) + 19.5
The period, T is given by 2pi/w = 2pi/(pi/3) = 6 min. 
h(3) = -17.5*cos(pi) + 19.5 = 17.5 + 19.5 = 37 m (maximum height)
A graph of the function is attached.
*[illustration FW.png]