A person is riding a ferris wheel that turns at a constant speeed. The lowest point of the ferris wheel is at ground level. Another person is standing at the side of the wheel on a platform 4m above the ground. She notes the times that the person on the wheel is at the same level as she. The intervals between two successive times are alternately 6s and 18s.

Question

A person is riding a ferris wheel that turns at a constant speeed.  The lowest point of the ferris wheel is at ground level.  Another person is standing at the side of the wheel on a platform 4m above the ground.  She notes the times that the person on the wheel is at the same level as she.  The intervals between two successive times are alternately 6s and 18s.

a)what is the period of rotation of the ferris wheel?

b)what is the radius of the wheel? Determine an equation for this function.

Steve · Answer

It appears that the person on the wheel is at height 4 at t=6 and t=18

Since the person on the wheel is at the lowest point at t=0, we have

y = r(1-cos(t))

Since t=6 going up, t=18+6=24 when the person is back on the ground. So, the period is 24 and the height of 4 is at 1/4 of a revolution.

y = r(1-cos(pi/12 t))

Since y=4 at t=6, we have r=4, and

y = 4(1-cos(pi/12 t))

http://www.wolframalpha.com/input/?i=plot+y%3D4%281-cos%28pi%2F12+x%29%29%2Cy%3D4