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?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 67E
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