Ferris Wheel #2

Question

Another Ferris Wheel has a radius of 25 feet and reaches a maximum height of 55 feet above the ground. From the location of your seat when the wheel starts turning, it takes you 6 seconds to reach the top. It takes 16 seconds for the wheel to make a full rotation. Sketch at graph (you do not need to include it here to turn in – it is just to help you write an equation) and then answer the following questions.

a) What is an equation for your graph?

b) What do you notice about the amplitude and vertical shift of your graph as they relate to the Ferris Wheel itself?

c) Why does your minimum height have to be greater than zero for any Ferris Wheel?

Answer 1

h(t)= Asin(B(t-C)+D

D=(55+5)/2= 30=midline

A=55-30= 25=Amplitude

B= 2pi/period= 2pi/16=pi/8

C=horizontal shift=2

6 seconds from start to top when h(6)=55

25sin(pi/8(6-C)+30= 55

sin((pi/8)(6-C))=1

let y= ((pi/8)(6-C))

siny=1

y= sin^-1(1)= pi/2

(pi/8)(6-C)=pi/2

6-C=4

C=2

A=25,B=pi/8, C=2, D=30

h(t)= 25sin(pi/8)(t-2))+ 30

vertical shift = D-A= 30-25

Amplitude =max-D=55-30= 25