Answer
$2.86\times10^{8}m/s$.
Work Step by Step
The problem asks for a speed such that the value of $\gamma$ is $\frac{1}{\sqrt{1-u^{2}/c^{2}}}=\frac{1.00m}{0.3048m}=3.281$. That is the factor by which the length is contracted.
$u/c=\sqrt{1-(1/3.281)^2}=0.9524$
$u =0.9524(3.00\times10^{8}m/s) =2.86\times10^{8}m/s $
