Answer
0.9716c.
Work Step by Step
In the Earth’s reference frame, the pion’s average lifetime ($2.6\times10^{-8}s$) of the pion will be dilated, equation 26–1a.
Find the speed of the pion as the distance moved in the Earth frame divided by the dilated time.
$$v=\frac{d}{\Delta t}=\frac{d}{\Delta t_0}\sqrt{1-v^2/c^2}$$
$$v=c\sqrt{\frac{1}{1+(\frac{c\Delta t_0}{d})^2}}$$
$$v=c\sqrt{\frac{1}{1+(\frac{(3\times10^8 m/s)(2.6\times10^{-8}s)}{32m})^2}}=0.9716c$$