College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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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 Using the power series representation In(1 + x) = x - y = tan(0)x - g kvo cos(8) Σ n = 2 5-) x + 2/2 ( 1. - k² gx² ² cos² (0) 2vo g y = (tan(6) + kv Cos(0) ) x + ( n = 1 (-1)³” (1 – kx vocos (8) n-1 kx Vo cos(8) kgx³ 3v³ cos³(0) (-1)²+1(1- n-1 x² x³ x4 + 2 3 4 + n - k²gx² 4 cos* (0) 4v0 kx Vocos (8) n -1 < x < 1, verify that the trajectory can be rewritten as the following.
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Transcribed Image Text: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 Using the power series representation In(1 + x) = x - y = tan(0)x - g kvo cos(8) Σ n = 2 5-) x + 2/2 ( 1. - k² gx² ² cos² (0) 2vo g y = (tan(6) + kv Cos(0) ) x + ( n = 1 (-1)³” (1 – kx vocos (8) n-1 kx Vo cos(8) kgx³ 3v³ cos³(0) (-1)²+1(1- n-1 x² x³ x4 + 2 3 4 + n - k²gx² 4 cos* (0) 4v0 kx Vocos (8) n -1 < x < 1, verify that the trajectory can be rewritten as the following.
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