A 50 foot diameter Ferris Wheel makes a complete turn every 20 seconds. A rider's height above the ground can be given as a function of time t (in seconds).

Question

A 50 foot diameter Ferris Wheel makes a complete turn every 20 seconds. A rider's height above the ground can be given as a function of time t (in seconds). Assume that at time t=0, you are the absolute bottom of the wheel starting at 8 feet above ground.

 

a.write an equation using cosine.

 

b. how high is the rider after 8 seconds?

Answer 1

The equation is given by 

 

h = 33 - 25 cos (2πt/20)

 

Here the concept used is that the wheel turns one full round in 20 seconds which sweeps one full diameter.  The amplitude is 25 ft and so the highest point is going to be 58 ft and the lowest point is going to be 8 feet.

 

h = 33 - 25 cos (4π/5) = 28.23 ft.