# Homework Help: A question about 4-velocity vector in relativity

1. Jul 10, 2010

### m.medhat

1. The problem statement, all variables and given/known data
Hello ,
I have the book (An introduction to tensor calculus , relativity and cosmology) , this book defined the 4-velocity vector as :-

And this book stated that :-

How could we obtain (17.4) from (15.6) ???

Thanks ……..

2. Relevant equations

3. The attempt at a solution

2. Jul 10, 2010

### kuruman

Calculate the magnitude squared of the four-vector on the right side of 15.6. What do you get?

3. Jul 10, 2010

### m.medhat

i do that but i don't obtain the result (-c^2)
i still need help .

4. Jul 10, 2010

### kuruman

Show exactly what you did. You probably made a mistake somewhere.

5. Jul 10, 2010

### m.medhat

let (1-[v^2]/[c^2])^-1/2 = y
therefore ?:-
V = y (v,ic)
V^2 = (y^2) ([v^2] + [ic]^2)
then V^2 = [y^2] ([v^2]-c^2)
that's all.

i still need help , please .

6. Jul 10, 2010

### kuruman

You should have left the denominator alone instead of replacing it by 1/γ. All you need to do is simplify

$$\frac{v^2-c^2}{1-\frac{v^2}{c^2}}$$

7. Jul 15, 2010

### m.medhat

i understand the idea , thank you veryyyyyyyy much .