The value of γ needed for transformation between the two frames is 2.2942.
To transform the position, time, mass from one coordinate frame to another frame which moves with a speed v relative to the first, we need to calculate the Lorentz constant γ .
This is given by,
[tex] \gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}} [/tex]
Substitute [tex] 2.70*10^8 m/s [/tex] for v and [tex] 3.00*10^8 m/s [/tex] for c.
[tex] \gamma =\frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \\ =\frac{1}{\sqrt{1-\frac{(2.70*10^8 m/s)^2}{(3.00*10^8 m/s)^2}}} \\ =\frac{1}{\sqrt{0.19}} \\ =2.2942 [/tex]
The Lorentz factor needed for transforming the position and time coordinates from the given frame to the frame moving with a speed v relative to it is 2.2942
