Imagine a circle on the ground with point Q being where the circle touches the ground...

Now if the circle turns, Q moves further and further from the ground (following a circular path). The diameter of the circle is 100m. It takes 20mins for one revolution. At time=0s, Q is 0m from the ground. The circle then turns. What is the relationship between the time t from when the circle starts turning, and the distance d that Q is above the ground?

Thanks

Draw a picture of the system and you should be able to see that the height of the point Q above the ground is d = R(1-cosΘ) where R is the radius of the circle, and Θ is the angle of rotation of the wheel. Since Θ makes one complete revolution every 20 minutes, Θ =(2π/20)t = πt/10 where t is measured in minutes from the time at which Θ = 0.

Putting that together:

d = R(1-cosΘ) = 100[1-cos(πt/10)]