Air enters the converging nozzle at \(T_{1}=70^{\circ} \mathrm{F}\) and \(V_{1}=50 \mathrm{ft} / \mathrm{s}\). At the exit of the nozzle, \(V_{2}\) is given by

\[ V_{2}=\sqrt{V_{1}^{2}+2 c_{p}\left(T_{1}-T_{2}\right)} \]

where \(c_{p}=187 \mathrm{ft} \cdot \mathrm{lb} / \mathrm{lbm} \cdot{ }^{\circ} \mathrm{F}\) and \(T_{2}\) is the air temperature at the exit of the nozzle. Find the temperature \(T_{2}\) for which \(V_{2}=\) \(1000 \mathrm{ft} / \mathrm{s}\).

Figure P1.109

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