A ferris wheel has a radius of 10 m and th bottom of the wheel passes 1 meter above the ground

complete-revolution

#1

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 = PIt/10 radians
Plug this value in eq1
h(t) = 11-10Cos(PI
t/10)