How To Solve The Special Relativity Time Dilation
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Transcript of How To Solve The Special Relativity Time Dilation
![Page 1: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/1.jpg)
How to Solve the Special Relativity Time Dilation
Equation for VelocityA Mathematical Puzzle
![Page 2: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/2.jpg)
2
2
0
1cv
tt
Here is the equation to start with
![Page 3: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/3.jpg)
2
2
1
1215
cv
Put in the numbers you want. Note that t0 is the ship time, and t is the time for the stationary observer
![Page 4: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/4.jpg)
12
Now, switch the two terms by cross multiplying
2
2
1c
v
15
![Page 5: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/5.jpg)
12
2
2
1c
v
15
Now, switch the two terms by cross multiplying
![Page 6: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/6.jpg)
12
2
2
1c
v15
Now, switch the two terms by cross multiplying
![Page 7: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/7.jpg)
15
122
2
1c
v
Now, switch the two terms by cross multiplying
![Page 8: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/8.jpg)
Now, square both sides
15
122
2
1c
v
![Page 9: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/9.jpg)
Now, square both sides
2
15
12
2
2
2
1
c
v
![Page 10: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/10.jpg)
Simplify
225
1442
2
1c
v
![Page 11: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/11.jpg)
And convert to a decimal
64.02
2
1c
v
![Page 12: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/12.jpg)
Add to both sides
2
2
64.0c
v2
2
2
2
1c
v
c
v
![Page 13: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/13.jpg)
Simplify
2
2
64.0c
v2
2
2
2
1c
v
c
v
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Simplify
2
2
64.0c
v1
![Page 15: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/15.jpg)
Subtract from both sides
2
2
64.064.0c
v64.01
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Simplify
2
2
64.064.0c
v64.01
![Page 17: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/17.jpg)
Simplify
2
2
c
v64.01
![Page 18: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/18.jpg)
Simplify
2
2
c
v36.0
![Page 19: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/19.jpg)
Take the square root of both sides
2
2
c
v36.0
![Page 20: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/20.jpg)
Take the square root of both sides
c
v60.0
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Cross multiply the c
c
v60.0
![Page 22: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/22.jpg)
Cross multiply the c
v60.0 c
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Cross multiply the c
v60.0c
![Page 24: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/24.jpg)
Cross multiply the c
v60.0 c
![Page 25: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/25.jpg)
Cross multiply the c
v60.0 c
![Page 26: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/26.jpg)
You can leave this as your answer
v c60.0
OR
![Page 27: How To Solve The Special Relativity Time Dilation](https://reader034.fdocuments.in/reader034/viewer/2022050804/553829f04a79591b688b472c/html5/thumbnails/27.jpg)
Convert to a velocity in m/s
v )100.3(60.0 8
s
m
s
m8108.1