Call the height 'h", and the time-to-fall of the first object 't". Use g = 9.80665 m/s^2 for gravity, and assume no air resistance.
Then h = 0.5* g* t^2
and for the second object, h = 25 (t-2) + 0.5*g * (t-2)^2
Set those two equations equal, and I get t = 5.64106 seconds, and h = 156.031 meters.
Those numbers should be rounded off. If the velocity was 25.5 m/s, then h = 139.392 meters. And if I use 24.5 m/s, then h = 177.321. So the average is 158.4 +/- 19.0.
In other words, a 2% uncertainly in the initial velocity results in a 12% uncertainly in the height. This is not a good way to measure the height.