Barbara boards a Ferris wheel with a 50-foot radius. The center of the Ferris wheel is 60 feet above the ground. When Barbara boards, the Ferris wheel is at the bottom of its rotation. The angle swept out as Barbara rotates is measured from the 3 o'clock position. a) Define a function f that relates Barbara's vertical distance above the ground v (measured in feet) as a function of her angle of rotation, 0 (measured in radians) from the right side of the Ferris wheel. b) Suppose that the Ferris wheel rotates so that each cart moves at a constant rate of 8 feet per second and makes no stops. Express the distance traveled by Barbara s (in feet) as a function of the number of seconds t since the Ferris wheel began to turn. c) Express 0 the angle of rotation from the right side of the Ferris wheel in terms of t the number of seconds since the Ferris wheel began to turn.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Barbara boards a Ferris wheel with a 50-foot
radius. The center of the Ferris wheel is 60 feet
above the ground. When Barbara boards, the
Ferris wheel is at the bottom of its rotation. The
angle swept out as Barbara rotates is measured
from the 3 o'clock position.
a) Define a function f that relates Barbara's vertical
distance above the ground v (measured in feet) as
a function of her angle of rotation, 0 (measured in
radians) from the right side of the Ferris wheel.
b) Suppose that the Ferris wheel rotates so that
each cart moves at a constant rate of 8 feet per
second and makes no stops. Express the distance
traveled by Barbara s (in feet) as a function of the
number of seconds t since the Ferris wheel began
to turn.
c) Express O the angle of rotation from the right
side of the Ferris wheel in terms of t the number of
seconds since the Ferris wheel began to turn.
Transcribed Image Text:Barbara boards a Ferris wheel with a 50-foot radius. The center of the Ferris wheel is 60 feet above the ground. When Barbara boards, the Ferris wheel is at the bottom of its rotation. The angle swept out as Barbara rotates is measured from the 3 o'clock position. a) Define a function f that relates Barbara's vertical distance above the ground v (measured in feet) as a function of her angle of rotation, 0 (measured in radians) from the right side of the Ferris wheel. b) Suppose that the Ferris wheel rotates so that each cart moves at a constant rate of 8 feet per second and makes no stops. Express the distance traveled by Barbara s (in feet) as a function of the number of seconds t since the Ferris wheel began to turn. c) Express O the angle of rotation from the right side of the Ferris wheel in terms of t the number of seconds since the Ferris wheel began to turn.
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