Answer
The fish must spot the pelican at a minimum height of 3.1 meters in order to take evasive action.
Work Step by Step
Let's assume that the down direction is positive.
$y = \frac{1}{2}at^2$
$t = \sqrt{\frac{2y}{a}} = \sqrt{\frac{(2)(14.0 ~m)}{(9.80 ~m/s^2)}} = 1.69 ~s$
It takes a total time of 1.69 seconds for the pelican to reach the water from a height of 14.0 m.
In order to take evasive action, the fish can spot the pelican 1.49 seconds after the pelican has started the dive. This would allow the fish 0.20 seconds to take evasive action.
$y = \frac{1}{2}at^2 = \frac{1}{2}(9.80 ~m/s^2)(1.49 ~s)^2 = 10.9 ~m$
At t = 1.49 seconds, the pelican has fallen a distance of 10.9 meters, which is 3.1 meters above the water. The fish must spot the pelican at a minimum height of 3.1 meters in order to take evasive action.
