Problem $10\mathrm{.}138-$ Thrust and velocity at the engine nozzle exit in a jet engine

A pure jet engine propels an aircraft at $240\frac{m}{s}$ through air at $45$ kPa and $-13C.$ The inlet diameter of this engine is $1\mathrm{.}700$ m $,$ the compressor pressure ratio is $13,$ and the temperature at the turbine inlet is $557C.$ Determine the velocity at the exit of this engine's nozzle and the thrust produced. Assume ideal operation for all components and constant specific heats at room temperature. The properties of air at room temperature are $R=0\mathrm{.}287$kPa$*\frac{m^3}{k}g*K,c_p=1\mathrm{.}005k\frac{J}{k}g*K$ and $k=1\mathrm{.}4.$

The velocity at the exit of this engine's nozzle is $\frac{m}{s}.$

The thrust produced is $$ IN$.$