4) If a water wave of length L moves with velocity v in a body of water with depth d, then gL the velocity can be modeled by v = 2 πα tanh (“), where g is the acceleration due to gravity. a) Explain why the approximation v = gL is appropriate in deep water. b) When the water is shallow, d is small. For small x, tanh(x) can be approximated with it's tangent line at the origin. What is an approximation for v in shallow water? c) Find an expression/function that represents the acceleration of a wave as a function of time

Calculus: Early Transcendentals
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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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4) If a water wave of length L moves with velocity v in a body of water with depth d, then
gL
the velocity can be modeled by v =
2 πα
tanh (“), where g is the acceleration due
to gravity.
a) Explain why the approximation v =
gL
is appropriate in deep water.
b) When the water is shallow, d is small. For small x, tanh(x) can be approximated with
it's tangent line at the origin. What is an approximation for v in shallow water?
c) Find an expression/function that represents the acceleration of a wave as a function of
time
Transcribed Image Text:4) If a water wave of length L moves with velocity v in a body of water with depth d, then gL the velocity can be modeled by v = 2 πα tanh (“), where g is the acceleration due to gravity. a) Explain why the approximation v = gL is appropriate in deep water. b) When the water is shallow, d is small. For small x, tanh(x) can be approximated with it's tangent line at the origin. What is an approximation for v in shallow water? c) Find an expression/function that represents the acceleration of a wave as a function of time
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