A spherical steel rivet \((r=5 \mathrm{~mm})\), initially at a temperature of \(250^{\circ} \mathrm{C}\), falls from a tall building \((100 \mathrm{~m})\) through ambient air \((300 \mathrm{~K})\). The rivet's velocity and the heat transfer coefficient are given by:

\[\begin{gathered}v=g t \quad g \text {-gravitational acceleration } t-\text { time } \\\overline{N u_{d}}=50\left(1+v^{2 / 3}\right)\end{gathered}\]

Assuming the lumped capacitance formulation is a valid approximation for the rivet, what is the temperature of the rivet when it hits the ground \(4.5 \mathrm{~s}\) later?