Answer:
[tex]6.59\times 10^7m/s[/tex]
Explanation:
We are given that
Wavelength of red light=[tex]\lambda=635nm[/tex]
Wavelength of green light=[tex]\lambda'=510 nm[/tex]
We have to find the speed of physicist traveling according to his own testimony.
We know that
[tex]\frac{\lambda}{\lambda'}=\sqrt{\frac{1+\frac{v}{c}}{1-\frac{v}{c}}}[/tex]
Where [tex]c=3\times 10^8m/s[/tex]
Substitute the values
[tex]\frac{635}{510}=\sqrt{\frac{1+\frac{v}{c}}{1-\frac{v}{c}}}[/tex]
[tex]1.25=\sqrt{\frac{1+\frac{v}{c}}{1-\frac{v}{c}}}[/tex]
Squaring on both sides
[tex]1.5625=\frac{1+\frac{v}{c}}{1-\frac{v}{c}}[/tex]
[tex]1.5625-1.5625\frac{v}{c}=1+\frac{v}{c}[/tex]
[tex]1.5625-1=\frac{v}{c}+1.5625\frac{v}{c}=\frac{v}{c}(1+1.5625)[/tex]
[tex]0.5625=2.5625\frac{v}{c}[/tex]
[tex]v=\frac{0.5625c}{2.5625}=\frac{0.5625\times 3\times 10^8}{2.5625}[/tex]
[tex]v=6.59\times 10^7m/s[/tex]
