Table:
0
A
B
C
D
E
1
Condition/Parameter
Coordinate velocity v dx/dt in units of c
Velocity angle η in i-radians
Proper velocity w dx/dτ in units of c
Lorentz factor γ dt/dτ = E/mc 2
2
Momentum = ½mc ⇔ 0.5 map-lightyear/traveler-year
1/√5 ≅ 0.447
ln[(1 + √5)/2] ≅ 0.481
½
√5/2 ≅ 1.118
3
Rapidity of 0.5 hyperbolic radian
(e − 1)/(e + 1) ≅ 0.462
½
½(√e − 1/√e) ≅ 0.521
½(√e + 1/√e) ≅ 1.128
4
Momentum = mc ⇔ 1 map-lightyear/traveler-year
1/√2 ≅ 0.707
ln[1 + √2] ≅ 0.881
1
√2 ≅ 1.414
5
Rapidity of 1 hyperbolic radian
(e 2 − 1)/(e 2 + 1) ≅ 0.761
1
½(e − 1/e) ≅ 1.175
½(e + 1/e) ≅ 1.543
6
Kinetic energy = mc 2 ⇔ 2 map-years/traveler-year
√3/2 ≅ 0.866
ln[√3 + 2] ≅ 1.317
√3 ≅ 1.732
2
7
Momentum = 2mc ⇔ 2 map-lightyears/traveler-year
2/√5 ≅ 0.894
ln[2 + √5] ≅ 1.444
2
√5 ≅ 2.236
8
Rapidity of 2 hyperbolic radians
(e 4 −1)/(e 4 +1) ≅ 0.964
2
½(e 2 − 1/e 2 ) ≅ 3.627
½(e 2 + 1/e 2 ) ≅ 3.762

Questions and formulas:
Question: If the velocity angle is ln[(1 + √5)/2] ≅ 0.481, what is the condition/parameter?
Formula: UNIQUE(CHOOSECOLS(FILTER(A1:E1,C1="ln[(1 + √5)/2] ≅ 0.481"),1))
Formula2: UNIQUE(CHOOSECOLS(FILTER(A2:E8,C2:C8="ln[(1 + √5)/2] ≅ 0.481"),1))
Level: medium
Question: If the the condition/parameter is rapidity of 2 hyperbolic radians, what is the coordinate velocity v dx/dt in units of c?
Formula: UNIQUE(CHOOSECOLS(FILTER(A1:E1,A1="Rapidity of 2 hyperbolic radians"),2))
Formula2: UNIQUE(CHOOSECOLS(FILTER(A2:E8,A2:A8="Rapidity of 2 hyperbolic radians"),2))
Level: medium
Question: If the coordinate velocity v dx/dt in units of c is (e 2 − 1)/(e 2 + 1) ≅ 0.761, what is the velocity angle η in i-radians?
Formula: UNIQUE(CHOOSECOLS(FILTER(A1:E1,B1="(e 2 − 1)/(e 2 + 1) ≅ 0.761"),3))
Formula2: UNIQUE(CHOOSECOLS(FILTER(A2:E8,B2:B8="(e 2 − 1)/(e 2 + 1) ≅ 0.761"),3))
Level: medium
Question: What is the coordinate velocity v dx/dt in units of c total number if the velocity angle η in i-radians is ln[2 + √5] ≅ 1.444?
Formula: ROWS(UNIQUE(FILTER(B1, C1="ln[2 + √5] ≅ 1.444")))
Formula2: ROWS(UNIQUE(FILTER(B2:B8, C2:C8="ln[2 + √5] ≅ 1.444")))
Level: medium
Question: If the condition/parameter is rapidity of 1 hyperbolic radian, what is the proper velocity w dx/dτ in units of c?
Formula: UNIQUE(CHOOSECOLS(FILTER(A1:E1,A1="Rapidity of 1 hyperbolic radian"),4))
Formula2: UNIQUE(CHOOSECOLS(FILTER(A2:E8,A2:A8="Rapidity of 1 hyperbolic radian"),4))
Level: medium
Question: If the lorentz factor γ dt/dτ = e/mc 2 is √5 ≅ 2.236, what is the proper velocity w dx/dτ in units of c?
Formula: UNIQUE(CHOOSECOLS(FILTER(A1:E1,E1="√5 ≅ 2.236"),4))
Formula2: UNIQUE(CHOOSECOLS(FILTER(A2:E8,E2:E8="√5 ≅ 2.236"),4))
Level: medium