A Ferris wheel takes 100 s to make 4 revolutions. The maximum height of the Ferris wheel above the ground is 47 m and its diameter is 46 m.

Question

A Ferris wheel takes 100 s to make 4 revolutions. The maximum height of the Ferris wheel above the ground is 47 m and its diameter is 46 m. Assuming a > 0 and the ride starts at the minimum at t = 0 s, determine the function h(t)=a sin[2pi/b(t-c)]+d

1. Identify the values of a, b, and d There should be six digits in your answer.
2. The value of c, rounded to the nearest hundredth, is

Please help I'm studying and very confused

Answer 1

period = 4 revolutions in 100 seconds = 4/100 = 1/25 = B/2pi

b = 2pi/25

max height = 47, diameter = 46 m

min height = 1 m

midline = d = (47+1)/2 = 48/2 = 24

a = 46/2 = 23

f(t) = asin((2pi/b)(t-c) +d is the general formula

ride starts at t=0, f(0) = 1 = minimum height

= 1 = asin((2pi/b)(t-c) + 24

asin((2pi/b)(t-c)) = -23

a=23

23sin((2pi/b)(-c) = -23

sin((2pi/b)(-c) =-1

(2pi/b)(-c) = 270 degrees = 3pi/2

-2c/b = 3/2

b=2pi/25

-2c/(2pi/25) = 3/2

-2c(25/2pi) = 3/2

-c(25/pi) = 3/2

-c = (3/2)(pi/25) = 3pi/50

c = -3pi/50

f(t) = 23sin((2pi/(2pi/25)(t+3pi/50)) + 24

f(t) = 23sin((25)(t+3pi/50) +24

a=23

d=24

c=-3pi/50= about -.19

b = 2pi/25

if you want c in decimal form

c= about-3(3.141593)/50

= about -.1885

= about -.19 rounded to nearest hundredth

this gets a little tedious in the calculations

no guarantees the above calculations are error free

check the answer

plug in t=0 and you should get minimum height = 1 meter

Answer 2

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