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1. The velocity, v, of an object moving through a fluid can be modeled by the drag equation dv -kv? dt where k is a constant. An object moving through the water has an initial velocity, vo, in the interval of 16 m/sec

1. The velocity, v, of an object moving through a fluid can be modeled by the drag equation dv -kv? dt where k is a constant. An object moving through the water has an initial velocity, vo, in the interval of 16 m/sec

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Polynomial Functions
Section3.5: Mathematical Modeling And Variation
Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...
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1. The velocity, v, of an object moving through a fluid can be modeled by the drag equation dv -kv? dt where k is a constant. An object moving through the water has an initial velocity, vo, in the interval of 16 m/sec <voS 20 m/sec. After 2.0 seconds, the velocity has decreased to v, in the interval of 8 m/sec < v, < 12 m/sec. а. Find the equation that models the velocity of the object, v at any time, t (choose a value of vo and v, from the given intervals). By using an appropriate analytical method, solve the derived model, explain the reason for the selection of the method and discuss the behavior of the velocity, v(t) for interval of 0sts 10 and t approaches to infinity. Compute the velocity of the object after 10 seconds by using the derived model in Part 1(a) with TWO (2) different numerical methods with step size, h = 2 seconds. Select the best numerical method to compute the velocity of the object and justify your answer by computing the percentage of relative error. b.
Transcribed Image Text:1. The velocity, v, of an object moving through a fluid can be modeled by the drag equation dv -kv? dt where k is a constant. An object moving through the water has an initial velocity, vo, in the interval of 16 m/sec <voS 20 m/sec. After 2.0 seconds, the velocity has decreased to v, in the interval of 8 m/sec < v, < 12 m/sec. а. Find the equation that models the velocity of the object, v at any time, t (choose a value of vo and v, from the given intervals). By using an appropriate analytical method, solve the derived model, explain the reason for the selection of the method and discuss the behavior of the velocity, v(t) for interval of 0sts 10 and t approaches to infinity. Compute the velocity of the object after 10 seconds by using the derived model in Part 1(a) with TWO (2) different numerical methods with step size, h = 2 seconds. Select the best numerical method to compute the velocity of the object and justify your answer by computing the percentage of relative error. b.
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