AP Precalculus FRQ: A ride on a Ferris wheel

Question 3, Modeling a Periodic Context (no calculator), 6 pointsAbout 18 minutes · No calculator

A Ferris wheel has a diameter of 40 meters, and its center is 25 meters above the ground. The wheel turns at a constant speed and completes one full rotation every 8 minutes. A rider boards a car at the lowest point of the wheel at time

t

= 0

minutes. The sinusoidal function

h

models the rider's height above the ground, in meters, as a function of time

t

, in minutes.

(A) The graph of

h(t)

and its dashed midline for two full cycles is shown. Five points,

F

G

J

K

and

P

, are labeled on the graph. No scale is indicated. Determine possible coordinates

(t, h(t))

for the five points

F

G

J

K

and

P

. 2 points

(B) The function

h

can be written in the form

h(t)

= a\sin(b(t + c)) + d

. Find values of the constants

a

b

c

and

d

. 2 points

h

in part A. The

t

-coordinate of

J

t_1

, and the

t

-coordinate of

K

t_2

. (i) On the interval

(t_1, t_2)

, which of the following is true about

h

? a.

h(t)

is greater than 25 and increasing. b.

h(t)

is greater than 25 and decreasing. c.

h(t)

is less than 25 and increasing. d.

h(t)

is less than 25 and decreasing. (ii) Describe how the rate of change of

h

is changing on the interval

(t_1, t_2)

. Give a reason for your answer. 2 points