To State:
Whether the height of a dropped basketball over time be modelled by a trigonometric function. If yes, write the function, if not, explain why not.
No. The maximum height of a basketball steadily decreases with each bounce and such a decrease requires use of exponential function along with trigonometric and modulus functions to model.
Given:
A basketball is dropped from a height of
Concepts Used:
The maximum height of a dropped basketball reduces after each bounce depending on the rate of loss of energy at each bounce.
Description:
The situation can be modelled by a sinusoid with an exponentially decreasing amplitude. Since the height of the basketball is never negative, the said function has to be inside a modulus function.
Conclusion:
The height of dropped basketball cannot be modelled by a simple trigonometric function.
Chapter 10 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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