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

College Physics
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Chapter1: Units, Trigonometry. And Vectors
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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.
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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