What is the Magnitud of F in Newtons?

Question

A Chinook salmon has a maximum underwater speed of 3.0 m/s, and can jump out of the water vertically with a speed of 6.3 m/s. A record salmon has a length of 1.5 m and a mass of 63 kg. When swimming upward at constant speed, and neglecting buoyancy, the fish experiences three forces: an upward force F exerted by the tail fin, the downward drag force of the water, and the downward force of gravity. As the fish leaves the surface of the water, however, it experiences a net upward force causing it to accelerate from 3.0 m/s to 6.3 m/s. Assuming that the drag force disappears as soon as the head of the fish breaks the surface and that F is exerted until 2/3 of the fish's length has left the water, determine the magnitude of F.

Answer 1

F is exerted over a distance L=1 m and accelerates the fish from v1=3.0 to v2=6.3 m/s. We neglect buoyancy and drag, so F = m(g+A), where A is the acceleration. The kinetic energy change due to A is 0.5*m(v2^2-v1^2)=967 J; so the equivalent F*L = 967 J, and total F = 967 N + mg = 1584 N.