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 5.2 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 5.2 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.
please help im stuck!
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Verified answer
The force has done a work of F x d where d = [2/3] [1.5] m = 1m.
This work is used to increase the kinetic energy of the fish = 0.5 m [v^2 - u^2] and also to increase its potential energy of mg d where d = 1 m.
F*1 = 0.5 m [v^2 - u^2] + mg
F / m = 0.5* 18.04 + 9.8
F / m = 18.82
F = 18.82 x 63 = 1185.66 N
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vf^2 - vi^2 = 2ax
a = (vf^2 - vi^2) / 2x
x is 2/3 the salmon's length, l, so
net force = ma = 3m (vf^2 - vi^2) / 4l
force of tail fin = net force + weight
= 3m (vf^2 - vi^2) / 4l + mg
They give you the mass, the final and initial velocities, and the length. You know g. Plugnchug.