A projectile fired from the ground follows the trajectory given by the following equation, where v is the initial speed, is the angle of projection, g is the acceleration due to gravity, and k is the drag factor caused by airresistance.y = tan(0) +y = (tan(0))xUsing the power series representation In(1 + x) = x -y = tan(0)x -gkvo cos(8)Σn = 25-) x + 2/2 ( 1.-k²gx²² cos² (0)2vogy = (tan(6) + kv Cos(0) ) x + (n = 1(-1)³” (1 –kxvocos (8)n-1kxVo cos(8)kgx³3v³ cos³(0)(-1)²+1(1-n-1x² x³ x4+2 3 4+n-k²gx²4 cos* (0)4v0kxVocos (8)n-1 < x < 1, verify that the trajectory can be rewritten as the following.

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A projectile fired from the ground follows the trajectory given by the following equation, where v is the initial speed, is the angle of projection, g is the acceleration due to gravity, and k is the drag factor caused by air resistance. y = (tan(0) - + y = (tan(0))x - g kv cos(8), Using the power series representation In(1 + x) = x - y =tan(8)x - 57 ) x + 2/22 (1. In n = 2 00 9 y = (tan(0) + kv Cos(6) ) x + ( gx² 2v² cos² (0) (-1)"(1- cos (8) n-1 kx % cos(e) -*² +*²³-X² + 2 kgx³ 3v³ cos (0) (-1)"+¹1- n-1 21 - ..., 1

A projectile fired from the ground follows the trajectory given by the following equation, where v is the initial speed, is the angle of projection, g is the acceleration due to gravity, and k is the drag factor caused by air resistance. y = (tan(0) - + y = (tan(0))x - g kv cos(8), Using the power series representation In(1 + x) = x - y =tan(8)x - 57 ) x + 2/22 (1. In n = 2 00 9 y = (tan(0) + kv Cos(6) ) x + ( gx² 2v² cos² (0) (-1)"(1- cos (8) n-1 kx % cos(e) -² +²³-X² + 2 kgx³ 3v³ cos (0) (-1)"+¹1- n-1 21 - ..., 1

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 55P

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