A normal shock is observed to move through a constant$-$area tube into air at rest at $25C$ and $101$kPa. The velocity of the air behind the wave is measured to be $150\frac{m}{s}.$ Calculate:

$($a$)$ The shock velocity. Hint $($use if necessary$)$: Relate $M_1$ and $V.$ Use trial and error to find $M_1.$

$($b$)$ The stagnation temperature behind the shock in the stationary reference frame

$($c$)$ The static and stagnation pressures behind the shock in the moving reference frame