Airplanes can be launched from aircraft carriers by means of a catapult as shown below. The catapult is a well$-$insulated cylinder fitted with a frictionless piston. The piston is connected to the airplane by a cable. The cylinder is loaded with a high$-$pressure steam at $450C$ and $15$MPa which very rapidly expands to $0\mathrm{.}35$MPa. In this final state, water is present as both vapor and liqud. As the gas expands, the piston is driven back, which causes the plane to accelerate forward.

Neglecting friction, the mass of the piston and cable, and any thrust from the airplane engines, to what speed $(m\frac{i}{h}r)$ can this catapult accelerate a $30,000kg$ plane from rest if $300kg$ of superheated steam at $450C$ are supplied? $(252m\frac{i}{h}r)$