Calculating lifetime of a moving pion

[crh]

Homework Statement

What is the speed of a pion if its average lifetime is measured to be 4.91E-8s? At rest, its average lifetime is 2.60E-6s. What is the particle's lifetime at rest?

Homework Equations

$$\Delta t$$ = $$\Delta t₀$$ / $$\sqrt{1-(v²/c²}$$

The Attempt at a Solution

I don't want to type in all the numbers in the equation so I will tell you where they go.
$$\Delta t$$=4.91E-8s
$$\Delta t₀$$=2.60E-8s

I have everything plugged into where it needs to go, I just can't derive the answer. I am needing to find "v" in terms of "c", if that makes sense. My answer will be v= #.##c
Can someone help me.

 

[CompuChip]

Well, you have the relation
$$\Delta t = \Delta t_0 / \sqrt{1 - v^2 / c^2}$$
(click that to see the LaTeX code by the way, you'll see it's much easier than <sup>and <sub>)

You have $\Delta t$ and [itex]\Delta t_0[/tex], so basically it comes down to applying your math skills to solve for <i>v</i>. <br /> <br /> [Hint: let $\beta = v / c$ and solve for beta, that will give you the velocity already expressed in <i>c</i> ].<br /> <br /> [Second hint: If you don't see how to solve the equation right away, let $x = \sqrt{1 - \beta^2}$ and solve for x first.][/itex]</sub></sup>