**A ferris wheel has a radius of 10 m and th bottom of the wheel passes 1 meter above the ground. If the ferris wheel makes one complete revolution every 20 seconds, find an eqution that gives the height above the ground of a person on the ferris wheel as a function of time. Assume the person starts at the bottom of the ferris wheel.**

**Answer:**

Let’s say the height of a person on ferris wheel at time t is h (shown by point A)

To calculate h, we need to find out length CD

If angle ACD = θ (which is a function of time, t)

then, CD = 10Cosθ

therefore, h = length OD = OC - CD = 11-10Cosθ

h = 11-10Cosθ eq1

Now, we need to find out how θ is changing as a function of time, t

Since, ferris wheel makes a complete revolution (360 deg turn) in 20 sec

This means θ(t) = (360/20)*t = 18t in degrees
Let’s write the angle in radians: since 180 deg = PI radians => 1 deg = PI/180 radians
therefore, θ(t) = 18t*PI/180 = PI

*t/10 radians*

Plug this value in eq1

h(t) = 11-10Cos(PIt/10)

Plug this value in eq1

h(t) = 11-10Cos(PI