To determine the pelican's initial speed we first need to determine the time that elapsed before the fish hit the water.
The fish was dropped from a height of 4.6 m and it only had a horizontal velocity initially. The acceleration due to gravity is 9.8 m/s^2. The relation between the initial velocity, acceleration, time and distance traveled for an object is s = u*t + (1/2)a*t^2
=> 4.6 = 0*t + (1/2)*9.8*t^2
=> t^2 = 4.6*2/9.8
=> t = (sqrt 46)/7 s
The fish hit the water after (sqrt 46)/7 seconds. In this duration of time it traveled 6.8 m horizontally.
The horizontal speed of the fish was 6.8*7/sqrt 46 = 7.01 m/s.
As the fish had the same horizontal speed as the pelican that dropped it, the speed of the pelican was also 7.01 m/s