Answer
The height of the roof is 3.2 meters.
Work Step by Step
Let's suppose that one drop falls every $t$ seconds. The second drop has been falling for 3t seconds while the third drop has been falling for 2t seconds. The difference in their vertical displacement is 1.0 meter. Therefore;
$\frac{1}{2}g(3t)^2-\frac{1}{2}g(2t)^2 = 1.0~m$
$2.5gt^2 = 1.0~m$
$gt^2 = \frac{1.0~m}{2.5}$
The first drop hits the ground in 4t seconds. We can find the height $h$ that the first drop has fallen;
$h = \frac{1}{2}g(4t)^2$
$h = 8gt^2$
$h = (8)(\frac{1.0~m}{2.5})$
$h = 3.2~m$
The height of the roof is 3.2 meters.
