As a fish jumps vertically out of the water, assume that only two significant fo

Question

As a fish jumps vertically out of the water, assume that only two significant forces act on it: an upward force F exerted by the tail fin and the downward force due to gravity. A record Chinook salmon has a length of 1.50 m and a mass of 55.0 kg. If this fish is moving upward at 3.00 m/s as its head first breaks the surface and has an upward speed of 6.40 m/s after two-thirds of its length has left the surface, assume constant acceleration and determine the following.

a) the magnitude of the force F during this interval.

Explanation / Answer

Consider the three stages of the fish's movement: 1) The fish is below the surface but not touching it. The forces are in equilibrium, and the fish is moving at a constant speed of 3 m/s. F = mg + D 2) The fish is touching the surface. Only F and mg are acting. Since F is larger than mg, the fish accelerates. 3) The fish is 2/3(1.5 m) = 1 m above the surface. Only mg is acting. The fish stops accelerating. Between stage 2 and 3, the fish accelerates from 3 m/s to 7.1 m/s over a distance of 1 m. Therefore, the acceleration is: v(f)^2 = v(i)^2 +2ad (7.1 m/s)^2 = (3 m/s)^2 + 2a(1 m) a = 20.705 m/s^2 While the fish is accelerating, the only forces are F and mg, so F(net) = ma F + mg = ma F + (56 kg)(9.8 m/s^2) = (56 kg)(20.705 m/s^2) F = 610.68 N

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