Final answer:
To calculate the velocity of the fish relative to the water when it hits the water, we can use the principle of conservation of energy. By equating the initial potential energy to the final kinetic energy, we can solve for the velocity of the fish relative to the water.
Step-by-step explanation:
To calculate the velocity of the fish relative to the water when it hits the water, we can use the principle of conservation of energy.
First, we need to find the initial potential energy of the fish when it is 5.00 m above the water surface. The potential energy is given by the equation PE = mgh, where m is the mass of the fish, g is the acceleration due to gravity, and h is the height.
Next, we can calculate the final kinetic energy of the fish right before it hits the water. The kinetic energy is given by the equation KE = (1/2)mv^2, where m is the mass of the fish and v is the velocity of the fish relative to the water.
Finally, we can equate the initial potential energy to the final kinetic energy and solve for the velocity of the fish relative to the water.
Let's assume the mass of the fish is 1 kg.
Given: g = 9.8 m/s^2, h = 5.00 m
First, calculate the initial potential energy:
PE = (1 kg)(9.8 m/s^2)(5.00 m)
PE = 49 J
Next, calculate the final kinetic energy:
KE = (1/2)(1 kg)(v^2)
KE = (1/2)v^2
Equating the initial potential energy to the final kinetic energy:
49 J = (1/2)v^2
v^2 = (2)(49 J)
v^2 = 98 J
v = sqrt(98 J) = 9.90 m/s
Therefore, the velocity of the fish relative to the water when it hits the water is 9.90 m/s.