Answer
The water speed as it leaves the nozzle is 12 m/s.
Work Step by Step
$y = y_0 + v_0t + \frac{1}{2}at^2$
$v_0 = \frac{y - y_0 - \frac{1}{2}at^2}{t}$
$v_0 = \frac{0 ~m - 1.8 ~m - \frac{1}{2}(-9.8 ~m/s^2)(2.5 ~s)^2}{2.5 ~s}$
$v_0 = 12 ~m/s$
The water speed as it leaves the nozzle is 12 m/s.
