Answer
$\beta = 0.866$
Work Step by Step
We can find $\gamma$:
$E = \gamma~mc^2 = 2.00~E_0$
$\gamma~E_0 = 2.00~E_0$
$\gamma = 2.00$
We can find $\beta$:
$\gamma = \frac{1}{\sqrt{1-\beta^2}}$
$1-\beta^2 = \frac{1}{\gamma^2}$
$\beta^2 = 1-\frac{1}{\gamma^2}$
$\beta = \sqrt{1-\frac{1}{\gamma^2}}$
$\beta = \sqrt{1-\frac{1}{(2.00)^2}}$
$\beta = 0.866$
