Trigonometry - A Ferris Wheel that has a radius 60 metres and is raised 10 metres from the ground, takes 32 minutes to complete one revolution.

Question

A Ferris Wheel that has a radius 60 metres and is raised 10 metres from the ground,

takes 32 minutes to complete one revolution.

The height above ground of a person riding on this Ferris wheel follows a function

of the form

H(t) = a sin(b(t + c)) + d:

Here, H is used to denote the height above the ground of the person in metres, and

t is the time in minutes after they got on the Ferris wheel.

(a) Complete the function H by nding the amplitude, period, horizontal shift,

and vertical shift of the function.

(b) Use H to complete the following table and then graph your function.

Time (minutes) 0 4 8 12 16 20 24 28 32

Height (metres)

(c) Use your graph to approximate length of time that a person is more than 100

metres above the ground in a single revolution.

Answer 1

h(t)=asinb(t+c) +d

h(t) = 60sin((pi/16)(t+24)+70

d=10+60=70=midline= average height= average of max & min =(130+10)/2 =140/2=70

a=60= radius

b=2pi/period=2pi/32 =pi/16

h(0)=10, where sine of the angle, sin(3pi/2), =-1, when h=10= minimum height

pit/16+pic/16=3pi/2=24pi/16

pic=24pi

c=24

or c= -8

c=24 or -8