The ant is initially at the point P on the wheel, but the wheel is spun at a constant speed so that it moves around in circles counterclockwise, making 1 full revolution each minute. As a result, the ant's height as a function of time t (measured in minutes) can be modelled using an equation of the form h(t) = A+ B sin(2rt) + C cos(27t). (a) is at the points P, Q, R and S. Identify the times during the first minute of spinning at which the ant ). Given that the bike wheel has a radius of 1ft, identify the heights of the points Q, R and S. Then use this and your answer to (a) to find the values of A, B and C so that h(t) models the ant's height for all t. (b) (c) velocity). Find the rate of change of the ant's height (i.e. the ant's vertical (d) At what time(s) (in the first minute) is the ant's vertical velocity 0?
The ant is initially at the point P on the wheel, but the wheel is spun at a constant speed so that it moves around in circles counterclockwise, making 1 full revolution each minute. As a result, the ant's height as a function of time t (measured in minutes) can be modelled using an equation of the form h(t) = A+ B sin(2rt) + C cos(27t). (a) is at the points P, Q, R and S. Identify the times during the first minute of spinning at which the ant ). Given that the bike wheel has a radius of 1ft, identify the heights of the points Q, R and S. Then use this and your answer to (a) to find the values of A, B and C so that h(t) models the ant's height for all t. (b) (c) velocity). Find the rate of change of the ant's height (i.e. the ant's vertical (d) At what time(s) (in the first minute) is the ant's vertical velocity 0?
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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Transcribed Image Text:An ant is sitting on the rim of a bike wheel suspended 0.5ft in the air (the
circle shown below is meant to symbolize the bike wheel).
R
S
P
0.5f
The ant is initially at the point P on the wheel, but the wheel is spun at a constant
speed so that it moves around in circles counterclockwise, making 1 full revolution
each minute. As a result, the ant's height as a function of time t (measured in
minutes) can be modelled using an equation of the form
h(t) = A+ B sin(2nt) + C cos(2nt).
(a)
Identify the times during the first minute of spinning at which the ant
is at the points P, Q, R and S.
Given that the bike wheel has a radius of 1ft, identify the heights of
(b)
the points Q, R and S. Then use this and your answer to (a) to find the values
of A, B and C so that h(t) models the ant's height for all t.
(c)
velocity).
Find the rate of change of the ant's height (i.e. the ant's vertical
At what time(s) (in the first minute) is the ant's vertical velocity 0?
(d)
Does your answer make sense based on the picture?
7.
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