math
posted by Melissa .
Matthew is riding a ferris wheel at a constant speed of 10km/h. The boarding height for the wheel is 1m, and the wheel has a radius of 7m. What is the equation for the function that describes Matthews height in the terms of time, assuming Matthew starts at the highest point on the wheel

center of wheel is 1 + 7 = 8 m above ground
cos (2 pi t/T) is max of +1 when t = 0
so h = 8 + 7 cos (2 pi t/T)
what is T, the period or time to go 2 pi radians?
speed = 10,000 meters/3600 seconds
= 2.78 m/s
distance around = 2 pi r = 2 pi*7 = 44 m
so
T = 44m/2.78m/s = 15.8 seconds
so
h = 8 + 7 cos (2 pi t/15.8)