Precalculus Discussion Post Question NEED ASAP

Question

A Ferris wheel is 28 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 16 minutes. The function h(t) gives a person’s height in meters above the ground t minutes after the wheel begins to turn.

a. Find the amplitude, midline, and period of h(t).

Enter the exact answers.

Amplitude: A=

meters

Midline: h=

meters

Period: P=

minutes

b. Assume that a person has just boarded the Ferris wheel from the platform and that the Ferris wheel starts spinning at time t=0. Find a formula for the height function h(t).

Hints:

What is the value of h(0)?

Is this the maximum value of h(t), the minimum value of h(t), or a value between the two?

The function sin(t) has a value between its maximum and minimum at t=0 , so can h(t) be a straight sine function?

The function cos(t) has its maximum at t=0, so can h(t) be a straight cosine function?

c. If the Ferris wheel continues to turn, how high off the ground is a person after 60 minutes?

Answer 1

amplitude = 14 = A

midline is h=15 = D

period = 16

period = 2pi/B =16

B = 2pi/16 = pi/8

h(t) = Asin(Bt+C) + D, where A=14, B=pi/8, C=-pi/2, D=15

h(t) = 14sin((pi/8)t-pi/2) + 15

or

h(t) =14cos((pi/8)t +pi) +15

h(60)= 14cos((60pi/8+pi) +15

=14cos(17pi/2) + 15

=14cos(pi/2)+15

=14(0)+15

=15 feet high

h(60) = 14sin(60pi/8 -pi/2) +15

=14sin(7pi)+15

=14sin(pi) +15

=14(0) +15

=15

in 60 minutes 60/16 = 15/4 =3 3/4 revolutions

it's at the midline of 15 feet high

in half a revolution, the height is 29 feet

in a quarter or 3/4 revolution the height is 15 feet

in a full revolution height is 1 foot