= Solution
In the frame in which the shock is stationary, the upstream gas approaches it with speed $V$, while the downstream gas recedes from it with speed $V-u_1$. The <Rankine-Hugoniot conditions for a perfect gas> are therefore
$$
\rho_0V=\rho_1(V-u_1),
$$
$$
p_0+\rho_0V^2
=p_1+\rho_1(V-u_1)^2,
$$
and
$$
\frac{\gamma p_0}{(\gamma-1)\rho_0}+\frac12V^2
=\frac{\gamma p_1}{(\gamma-1)\rho_1}
+\frac12(V-u_1)^2.
$$
These equations express conservation of mass flux, momentum flux, and total specific enthalpy respectively.
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