Final answer:
The velocity of the fish relative to the water when it hits the water is approximately 5.0 m/s downward.
Step-by-step explanation:
The velocity of the fish relative to the water when it hits the water can be calculated using the principles of projectile motion. When the fish falls, it will have both a horizontal and vertical velocity component. The horizontal component will remain the same as the eagle's speed, while the vertical component will change due to gravity. Since the fish is falling vertically, we can use the equation:
vf = vi + at
where vf is the final velocity, vi is the initial velocity, a is the acceleration (in this case, due to gravity, -9.8 m/s^2), and t is the time it takes for the fish to fall. Since we know the fish falls 5.00 m below, we can set up the equation:
0 = 0 + (-9.8)t
Solving for t, we find that t = 0.51 s. Plugging this value back into the equation, we can find the final vertical velocity:
vf = vi + (-9.8)(0.51)
vf = -5.0 m/s
The negative sign indicates that the velocity is downward. Therefore, the velocity of the fish relative to the water when it hits the water is approximately 5.0 m/s downward.