Answer
$h=25.725m$
Work Step by Step
The height of the tower is the difference between the maximum height of the rock and the distance traveled by the rock between $t=1.5s$ and $t=2.5s$. The maximum height of the rock can be calculated with the equation $h=\frac{1}{2}gt^{2}$. The difference in height between the top of the tower and the maximum height of the rock can be calculated using the same equation.
$h=\frac{1}{2}gt^{2}_{max}-\frac{1}{2}gt^{2}_{1}=\frac{1}{2}g(t^{2}_{max}-t^{2}_{1})=\frac{1}{2}(9.8m/s^{2})[((2.5s)^{2}-(1.0s)^{2}]=25.725m$
