A ferris wheel takes 35 seconds to complete one revolution of the ride. The maximum height of the wheel is 25 metres and the minimum height is 3 metres. If a trigonometric equation were created (using radians) to represent the height of the ferris wheel as a function of time, what would be the value of 'b' for the equation, to the nearest hundredth?

Question

anonymous · Answer

The amplitude is the radius of the ferris wheel or (25-3)/2= 11 meters. 

The height will be a cosine function. 

The wheel has a constant of 3 meters + the radius of the wheel (11 meters). Which gives us 14 meters.

So far we have h=11cos(bt)+14

$$b=2\Pi/35$$ which gives us .18 radians per second when rounded to the nearest hundredth.

So the equation is h=11cos.18t+14

check

At zero seconds:

h=11cos(0)+14

h=11(1)+14  which gives us 25 meters

At 17.5 seconds:

h=11cos(.18)(17.5) + 14

h=11(-.999)+14 which gives us approximately 3 meters.

At 8.75 seconds:

h=11cos(.18)(8.75) +14

h=11(.004) + 14 which gives us approximately 14 meters.