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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 49.0 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 6.50 m/s after two-thirds of its length has left the surface, assume constant acceleration and determine the following.

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azikennamdi

The acceleration is computed at 16.625ms⁻²;

The Magnitude of Net Force = 814.625 N; and

The Magnitude of upward force exerted by tail fin = 1,294.825 N. See the explanation below.

What is the computation explaining the above answers?

Mass of the salmon fish = 49 kg

Length of the Salmon Fish = 1.5 m

g = 9.8 ms⁻²

[A] salmon's acceleration during the time interval N:

Downward Force on the fish is equal to the Force due to gravity and is given as:

F₂ = mg

= 49 * 9.8

= 480.2 N

The direction of movement of the fish is upward and the acceleration is constant. We are given two different velocities of fish at two different instances.

When the head breaks out of the water surface first:

Initial velocity = v₁ = 3 m/s

When two third of its body length is out = d = 1 m

Final Velocity = v₂ = 6.5 m/s

Using the third equation of motion:

2*a*d = v₂² - v₁²

a = (6.5² - 3²)/2*1

a = 16.625 ms⁻²

[B] magnitude of force F during this interval N = ?

We are assuming that F is the net force consisting of both the upward and the downward force.

According to Newton's 2nd law of motion, Force is given as:

F = ma

F = 49 kg * 16.625

F = 814.625 N

Magnitude of upward Force = Fₓ

Force Fₓ exerted by the tail fin of the fish is given by

F = Fₓ - F₂

=>   Fₓ = F + F₂

Fₓ = 814.625 + 480.2

Fₓ = 1294.825 N

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