$w_o = 62.5h \, \text{lb/ft}^2$

$F = \frac{1}{2} w_o h (3) = \frac{3}{2}(62.5h)h$

$F = 93.75h^2 \, \text{lb}$

$M = (\frac{1}{3}h) F = \frac{1}{3}h (93.75h^2)$

$M = 31.25h^3 \, \text{lb}\cdot\text{ft}$

$(\,f_b\,)_{max} = \dfrac{Mc}{I}$

$1200 = \dfrac{31.25h^3(12)(12/2)}{\dfrac{12(12^3)}{12}}$

$h = 9.73 \, \text{ft}$ *answer*