How to do linearization for physics in a horizontally launched projectile problem?

Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter1: Introduction And Vectors
Section: Chapter Questions
Problem 47P
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How to do linearization for physics in a horizontally launched projectile problem?

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