= Solution
{c}
The <special relativity> expression for <momentum> is $p=\gamma mv$, with <Lorentz factor> $\gamma=(1-v^2/c^2)^{-1/2}$. Equal <speeds> imply equal <Lorentz factors>, so the <pion> and <proton> <momenta> are in the ratio of their <rest masses>:
$$
\boxed{p_\pi=p_p\frac{m_\pi}{m_p}=400\frac{0.14}{0.94}
\simeq59.6\,\mathrm{GeV}/c.}
$$
The common dimensionless product is $\gamma v/c=p_p/(m_pc)=400/0.94\simeq425.53$, giving $\gamma\simeq425.53$ and $v/c\simeq0.99999724$.
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