Lorentz and Galilean Tranformations

[Icaro Amorim]

Homework Statement

At what speed v will the Galilean and Lorentz expressions for x differ by 0,10 percent?

Homework Equations

x_L= (x'+vt')/√(1-(v/c)²) (Lorentz Transformation)
x_G=x'+vt' (Galilean Tranformation)

The Attempt at a Solution

I've tried: x_G/x_L = √(1-(v/c)²) = 0,1%=0,1/100=10^(-3) => 1-(v/c)² = 10^(-6) => v = [√(1-10^-6)]*c~ 0,999999*c.
Where did I go wrong?

The result is 0,0447c according to the book (Introduction to

 

[maajdl]

xG/xL = √(1-(v/c)²) = 1-0,1%

"will differ by 0,10 percent"

not "will be 0.10 percent"

 

[Icaro Amorim]

Thanks, maajdl.

Greetings from Brazil.