Answer
The weight of the roof is $1.2\times 10^5~N$
Work Step by Step
We first convert the wind speed to units of m/s:
$v = (180~km/h)(\frac{1000~m}{1~km})(\frac{1~hr}{3600~s})$
$v = 50~m/s$
We then use Bernoulli's equation to find the pressure difference below the roof and above the roof.
$P_1 = P_2 + \frac{1}{2}\rho~v^2$
$P_1-P_2 = \frac{1}{2}\rho~v^2$
$P_1-P_2 = \frac{1}{2}(1.29~kg/m^3)~(50~m/s)^2$
$P_1-P_2 = 1612.5~N/m^2$
We then find the upward force exerted on the roof from the pressure difference.
$F = (P_1-P_2)~A$
$F = (1612.5~N/m^2)(6.2~m)(12.4~m)$
$F = 1.2\times 10^5~N$
Since the roof comes off the house, we can assume that the upward force exerted on the roof is equal to the weight of the roof. The weight of the roof is $1.2\times 10^5~N$.