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 61.0 kg. Of this fish is moving upward at 3.00 m/s as its head first breaks the surface and has an upward speed of 6.00 m/s after two-thirds of its length has left the surface, assume constant acceleration and determine the following:

a. the salmon's acceleration Incorrect
b. the magnitude of the force F during this interval N

Answer 1

(b) the magnitude of the force during the given interval is 225.7 N.

(a) The acceleration of the salmon fish is 13.5 m/s²

The given parameters;

• initial velocity of the fish, u = 3 m/s

• final velocity of the fish, v = 6 m/s

• length of the fish, L = 1.5 m

The distance traveled by the salmon fish when two-thirds of its length has left the surface;

$s = \frac{2}{3} \times 1.5 \ m = 1 \ m$

(a) The acceleration of the salmon fish is calculated as;

$v^2 = u^2 + 2as\\\\2as = v^2 - u^2\\\\a = \frac{v^2 - u^2}{2s} \\\\a = \frac{6^2 - 3^2}{2\times 1} \\\\a = 13.5 \ m/s^2$

(b) the magnitude of the force during the given interval is calculated as;

$\Sigma F_y = F_{up} - F_{down}\\\\F = ma - mg\\\\F = m(a - g)\\\\F = 61 (13.5-9.8)\\\\F = 225.7\ N$

Thus, the magnitude of the force during the given interval is 225.7 N.

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