Answer
The pole-vaulter's weight is $638N$.
Work Step by Step
We have $$PE_f-PE_0=-3.7\times10^3J$$ $$mg(h_f-h_0)=-3.7\times10^3J$$
From the given information, during the fall, $h_0=5.8m$ and $h_f=0$, so $h_f-h_0=-5.8m$
Therefore, $$mg=\frac{-3.7\times10^3J}{h_f-h_0}=638N$$ which is the pole-vaulter's weight.
