velocity vectors in two dimensions

`t_{f}=${t_{zero}}sec` left parenthesis, "X" left parenthesis, "t" Subscript, "z" "e" "r" "o" , Baseline , right parenthesis plus left parenthesis, StartFraction, "X" left parenthesis, "t" Subscript, "z" "e" "r" "o" , Baseline , right parenthesis Over 5 , EndFraction , right parenthesis , StartFraction, "y" Subscript, "v" , Baseline Over 2 , EndFraction minus 8 left parenthesis, StartFraction, "y" Subscript, "v" , Baseline Over 40 , EndFraction , right parenthesis , right parenthesis

ป้ายกำกับ:

equals

left parenthesis, 94.4 6 7 3 8 8 8 , 16.6 5 6 8 8 0 7 , right parenthesis

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instantanious displacement vector labels

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`||\vec{s}||=${s}` left parenthesis, StartFraction, "X" left parenthesis, "T" , right parenthesis Over 2 , EndFraction , StartFraction, "h" plus "Y" left parenthesis, "T" , right parenthesis Over 2 , EndFraction , right parenthesis

ป้ายกำกับ:

equals

left parenthesis, 12.8 7 , 36.5 2 1 2 1 9 , right parenthesis

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`${s_{x}}\hat{x}` left parenthesis, StartFraction, "X" left parenthesis, "T" , right parenthesis Over 2 , EndFraction , 0 , right parenthesis

ป้ายกำกับ:

equals

left parenthesis, 12.8 7 , 0 , right parenthesis

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`${s_{y}}\hat{y}` left parenthesis, 0 , "h" plus StartFraction, "Y" left parenthesis, "T" , right parenthesis minus "h" Over 2 , EndFraction , right parenthesis

ป้ายกำกับ:

equals

left parenthesis, 0 , 36.5 2 1 2 1 9 , right parenthesis

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time label at the top!

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`\Delta t = ${T} sec` left parenthesis, "x" Subscript, "v" , Baseline , "y" Subscript, "v" , Baseline plus left parenthesis, StartFraction, "y" Subscript, "v" , Baseline Over 7 , EndFraction , right parenthesis , right parenthesis

ป้ายกำกับ:

equals

left parenthesis, 34.9 8 4 7 0 9 5 , 63.4 5 4 7 8 3 7 , right parenthesis

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axis labels

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`x\ axis:\ x\ position\ (in\ m)` left parenthesis, left parenthesis, StartFraction, "x" Subscript, "z" "e" "r" "o" , Baseline Over 3 , EndFraction , right parenthesis , negative left parenthesis, StartFraction, "y" Subscript, "v" , Baseline Over 15 , EndFraction , right parenthesis , right parenthesis

ป้ายกำกับ:

equals

left parenthesis, 26.2 4 0 9 4 1 3 , negative 3.7 0 1 5 2 9 0 5 , right parenthesis

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`y\ axis\ =\ y\ position\ (in\ m)` left parenthesis, negative left parenthesis, StartFraction, "x" Subscript, "z" "e" "r" "o" , Baseline Over 10 , EndFraction , right parenthesis , StartFraction, "Y" left parenthesis, "t" Subscript, "v" , Baseline , right parenthesis Over 2 , EndFraction , right parenthesis

ป้ายกำกับ:

equals

left parenthesis, negative 7.8 7 2 2 8 2 4 , 27.7 6 1 4 6 7 9 , right parenthesis

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vertex vector labels

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`\vec{s_{max}}` left parenthesis, StartFraction, "s" Subscript, "v" "x" , Baseline Over 2 , EndFraction , StartFraction, "h" plus "y" Subscript, "v" , Baseline Over 2 , EndFraction , right parenthesis

ป้ายกำกับ:

equals

left parenthesis, 17.4 9 2 3 5 4 7 , 37.7 6 1 4 6 7 9 , right parenthesis

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`\vec{s_{max}}` left parenthesis, "x" Subscript, "v" , Baseline plus StartFraction, "x" Subscript, "z" "e" "r" "o" , Baseline Over 1.2 7 , EndFraction , "y" Subscript, "v" , Baseline plus 7 left parenthesis, StartFraction, "y" Subscript, "v" , Baseline Over 40 , EndFraction , right parenthesis , right parenthesis

ป้ายกำกับ:

equals

left parenthesis, 96.9 7 1 1 8 5 1 , 65.2 3 9 4 4 9 5 , right parenthesis

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`||\vec{s_v}||=${s_v}` left parenthesis, "x" Subscript, "v" , Baseline plus StartFraction, "x" Subscript, "z" "e" "r" "o" , Baseline Over 1.5 , EndFraction , "y" Subscript, "v" , Baseline plus 4 left parenthesis, StartFraction, "y" Subscript, "v" , Baseline Over 40 , EndFraction , right parenthesis , right parenthesis

ป้ายกำกับ:

equals

left parenthesis, 87.4 6 6 5 9 2 1 , 61.0 7 5 2 2 9 4 , right parenthesis

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`s_{v\theta}=${A_v}°` left parenthesis, "x" Subscript, "v" , Baseline plus StartFraction, "x" Subscript, "z" "e" "r" "o" , Baseline Over 1.5 , EndFraction , "y" Subscript, "v" , Baseline plus 2 left parenthesis, StartFraction, "y" Subscript, "v" , Baseline Over 40 , EndFraction , right parenthesis , right parenthesis

ป้ายกำกับ:

equals

left parenthesis, 87.4 6 6 5 9 2 1 , 58.2 9 9 0 8 2 6 , right parenthesis

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`s_{vx}=${x_{v}}\hat{x}` left parenthesis, "x" Subscript, "v" , Baseline plus StartFraction, "x" Subscript, "z" "e" "r" "o" , Baseline Over 1.5 , EndFraction , "y" Subscript, "v" , Baseline plus 0 left parenthesis, StartFraction, "y" Subscript, "v" , Baseline Over 40 , EndFraction , right parenthesis , right parenthesis

ป้ายกำกับ:

equals

left parenthesis, 87.4 6 6 5 9 2 1 , 55.5 2 2 9 3 5 8 , right parenthesis

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`s_{vy}=${s_{vy}}\hat{y}` left parenthesis, "x" Subscript, "v" , Baseline plus StartFraction, "x" Subscript, "z" "e" "r" "o" , Baseline Over 1.5 , EndFraction , "y" Subscript, "v" , Baseline minus 2 left parenthesis, StartFraction, "y" Subscript, "v" , Baseline Over 40 , EndFraction , right parenthesis , right parenthesis

ป้ายกำกับ:

equals

left parenthesis, 87.4 6 6 5 9 2 1 , 52.7 4 6 7 8 9 , right parenthesis

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`t_v=${t_v} sec` left parenthesis, "x" Subscript, "v" , Baseline plus StartFraction, "x" Subscript, "z" "e" "r" "o" , Baseline Over 1.5 , EndFraction , "y" Subscript, "v" , Baseline minus 4 left parenthesis, StartFraction, "y" Subscript, "v" , Baseline Over 40 , EndFraction , right parenthesis , right parenthesis

ป้ายกำกับ:

equals

left parenthesis, 87.4 6 6 5 9 2 1 , 49.9 7 0 6 4 2 2 , right parenthesis

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ซ่อน `Jake\ Bruner` left parenthesis, negative "x" Subscript, "v" , Baseline minus StartFraction, "x" Subscript, "z" "e" "r" "o" , Baseline Over 10 , EndFraction , 0 , right parenthesis

ป้ายกำกับ:

equals

left parenthesis, negative 42.8 5 6 9 9 1 9 , 0 , right parenthesis

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นิพจน์ 123:

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intercept/zeros label

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made by jake bruner, 11/3/20

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about 120 lines of equations

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นิพจน์ 127:

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i want to write the equation below in cartesian coords. this is in polar coords, and removing time from the parametric equation

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นิพจน์ 129: "y" equals StartFraction, "g" Over 2 "u" squared cos squared left parenthesis, "A" , right parenthesis , EndFraction times "x" squared plus tangent left parenthesis, "A" , right parenthesis times "x" plus "h"

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note: the tan here is from the uy=usinA and ux=ucosA

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นิพจน์ 131:

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นิพจน์ 132:

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นิพจน์ 133:

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ex: a= 80deg u = 30m/s, therefore ux = 5.21 m/s and uy = 29.5m/s

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ดำเนินการโดย

Start\vec "g" undefined equals negative 9.8 1 "m" / "s" squared

| | Start\vec "v" undefined | | equals 14.7 5 3 5 5 4 "m" / "s"

6.9 7 6 2 Start\hat "y" undefined "m" / "s"

13 Start\hat "x" undefined "m" / "s"

Start\vec "s" Subscript, "f" , Baseline undefined

| | Start\vec "s" Subscript, "f" , Baseline undefined | | equals 81.2 2 3 6 6

"s" Subscript, "f" theta , Baseline equals negative 14.2 5 4 7 5 2 degrees

"s" Subscript, "f" "x" , Baseline equals 78.7 2 2 8 2 4 Start\hat "x" undefined

"s" Subscript, "f" "y" , Baseline equals negative 20 Start\hat "y" undefined

"t" Subscript, "f" , Baseline equals 6.0 5 5 6 0 1 8

| | Start\vec "s" undefined | | equals 41.8 8 4 9 6 5

25.7 4 Start\hat "x" undefined

33.0 4 2 4 3 8 Start\hat "y" undefined

Delta "t" equals 1.9 8

"x" "a" "x" "i" "s" : "x" "p" "o" "s" "i" "t" "i" "o" "n" ( "i" "n" "m" )

"y" "a" "x" "i" "s" equals "y" "p" "o" "s" "i" "t" "i" "o" "n" ( "i" "n" "m" )

Start\vec "s" Subscript, "m" "a" "x" , Baseline undefined

| | Start\vec "s" Subscript, "v" , Baseline undefined | | equals 35.4 8 8 7 7 1

"s" Subscript, "v" theta , Baseline equals 45.4 3 7 3 6 4 degrees

"s" Subscript, "v" "x" , Baseline equals 34.9 8 4 7 0 9 Start\hat "x" undefined

"s" Subscript, "v" "y" , Baseline equals 35.5 2 2 9 3 6 Start\hat "y" undefined

"t" Subscript, "v" , Baseline equals 2.6 9 1 1 3 1 5