7. 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 P 0.5ft 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) is at the points P, Q, R and S. Identify the times during the first minute of spinning at which the ant (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. Given that the bike wheel has a radius of 1ft, identify the heights of (c) velocity). Find the rate of change of the ant's height (i.e. the ant's vertical (d) Does your answer make sense based on the picture? At what time(s) (in the first minute) is the ant's vertical velocity 0?
7. 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 P 0.5ft 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) is at the points P, Q, R and S. Identify the times during the first minute of spinning at which the ant (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. Given that the bike wheel has a radius of 1ft, identify the heights of (c) velocity). Find the rate of change of the ant's height (i.e. the ant's vertical (d) Does your answer make sense based on the picture? At what time(s) (in the first minute) is the ant's vertical velocity 0?
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section: Chapter Questions
Problem 30P: In this problem you are asked to find a function that models in real life situation and then use the...
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Question
Transcribed Image Text:7.
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
0.5ft
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(27t).
(a)
is at the points P, Q, R and S.
Identify the times during the first minute of spinning at which the ant
(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.
Given that the bike wheel has a radius of 1ft, identify the heights of
(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?
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