Answer
$2.86\times 10^8m/s$
Work Step by Step
We can find the required speed as follows:
$p^2=\frac{m^2v^2}{1-v^2/c^2}$
$\implies p^2(1-v^2/c^2)=m^2v^2$
This simplifies to:
$v=\frac{p}{\sqrt{m^2+p^2/c^2}}$
We plug in the known values to obtain:
$v=\sqrt{\frac{7.74\times 10^{20}}{(8.2\times 10^{11})^2+(7.74\times 10^{20}\times 3.00\times 10^8)^2}}$
$v=2.86\times 10^8m/s$
