Question

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

Answer 1

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)